examples/Chron1.0Radiocarbon.ipynb

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   "source": [
    "# Chron.jl standalone age-depth model using radiocarbon data\n",
    "\n",
    "This Jupyter notebook demonstrates an example age-depth model using [Chron.jl](https://github.com/brenhinkeller/Chron.jl). For more information, see [github.com/brenhinkeller/Chron.jl](https://github.com/brenhinkeller/Chron.jl) and [doi.org/10.17605/osf.io/TQX3F](https://doi.org/10.17605/osf.io/TQX3F)\n",
    "\n",
    "<a href=\"https://mybinder.org/v2/gh/brenhinkeller/Chron.jl/main?filepath=examples%2FChron1.0Radiocarbon.ipynb\" target=\"_blank\"><img src=\"https://static.mybinder.org/badge_logo.svg\" alt=\"Launch Binder notebook\" align=\"left\"></a> \n",
    "<p style=\"text-indent: 5px\">If running this notebook as an online Binder notebook and the webpage times out, click the badge at left to relaunch (refreshing will not work). Note that any changes will be lost! </p>\n",
    "\n",
    "Hint: `shift`-`enter` to run a single cell, or from the `Cell` menu select `Run All` to run the whole file. Any code from this notebook can also be copied and pasted into the Julia REPL or a `.jl` script.\n",
    "***\n",
    "\n",
    "## Load required Julia packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load (and install if necessary) the Chron.jl package\n",
    "try\n",
    "    using Chron\n",
    "catch\n",
    "    using Pkg\n",
    "    Pkg.add(\"Chron\")\n",
    "    using Chron\n",
    "end\n",
    "\n",
    "using Statistics, StatsBase, DelimitedFiles, SpecialFunctions\n",
    "using Plots; gr(); default(fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Enter sample information\n",
    "Paste your data in here!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Input the number of samples we wish to model (must match below)\n",
    "nSamples = 4\n",
    "\n",
    "# Make an instance of a ChronSection object for nSamples\n",
    "smpl = NewChronAgeData(nSamples)\n",
    "smpl.Name          = (\"Sample 1\", \"Sample 2\", \"Sample 3\", \"Sample 4\") # Et cetera\n",
    "smpl.Age_14C       = [ 6991,  7088,  7230,  7540,] # Measured ages\n",
    "smpl.Age_14C_sigma = [   30,    70,    50,    50,] # Measured 1-σ uncertainties\n",
    "smpl.Height[:]     = [ -355,  -380,-397.0,-411.5,] # Depths below surface should be negative\n",
    "smpl.Height_sigma[:]  = fill(0.01, nSamples) # Usually assume little or no sample height uncertainty\n",
    "smpl.Age_Sidedness[:] = zeros(nSamples) # Sidedness (zeros by default: geochron constraints are two-sided). Use -1 for a maximum age and +1 for a minimum age, 0 for two-sided\n",
    "smpl.Path = \"MyData/\" # Where do you want output files to be stored\n",
    "\n",
    "smpl.Age_Unit = \"Years BP\"; # Unit of measurement for ages\n",
    "smpl.Height_Unit = \"m\"; # Unit of measurement for Height and Height_sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that smpl.Height *must* increase with increasing stratigraphic height -- i.e., stratigraphically younger samples must be more positive. For this reason, it is convenient to represent depths below surface as negative numbers.\n",
    "\n",
    "***\n",
    "## Calculate calendar age PDFs for each sample\n",
    "Using the [IntCal 2013](https://doi.org/10.2458/azu_js_rc.55.16947) radiocarbon calibration curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "  888.315,574.001 889.938,583.173 891.561,590.448 893.184,596.106 894.807,600.045 896.43,603.071 898.053,605.362 899.675,607.074 901.298,608.335 902.921,608.657 \n",
       "  904.544,608.948 906.167,609.21 907.79,609.446 909.413,609.658 911.036,609.907 912.659,610.123 914.282,610.309 915.905,610.469 917.528,610.606 919.151,610.728 \n",
       "  920.774,610.832 922.397,610.918 924.019,610.991 925.642,611.052 927.265,611.124 928.888,611.179 930.511,611.222 932.134,611.255 933.757,611.281 935.38,611.302 \n",
       "  937.003,611.318 938.626,611.33 940.249,611.338 941.872,611.343 943.495,611.347 945.118,611.35 946.741,611.352 948.364,611.353 949.986,611.354 951.609,611.355 \n",
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       "  985.691,611.356 987.314,611.356 988.937,611.356 990.56,611.356 992.183,611.356 993.806,611.356 995.429,611.356 997.052,611.356 998.674,611.356 1000.3,611.356 \n",
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       "  1018.15,611.356 1019.77,611.356 1021.4,611.356 1023.02,611.356 1024.64,611.356 1026.26,611.356 1027.89,611.356 1029.51,611.356 1031.13,611.356 1032.76,611.356 \n",
       "  1034.38,611.356 1036,611.356 1037.62,611.356 1039.25,611.356 1040.87,611.356 1042.49,611.356 1044.12,611.356 1045.74,611.356 1047.36,611.356 1048.99,611.356 \n",
       "  1050.61,611.356 1052.23,611.356 1053.85,611.356 1055.48,611.356 1057.1,611.356 1058.72,611.356 1060.35,611.356 1061.97,611.356 1063.59,611.356 1065.21,611.356 \n",
       "  1066.84,611.356 1068.46,611.356 1070.08,611.356 1071.71,611.356 1073.33,611.356 1074.95,611.356 1076.58,611.356 1078.2,611.356 1079.82,611.356 1081.44,611.356 \n",
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       "  1520.29,611.356 1521.45,611.356 1522.61,611.356 1523.77,611.356 1524.93,611.356 1526.09,611.356 1527.25,611.356 1528.4,611.356 1529.56,611.356 1530.72,611.356 \n",
       "  1531.88,611.356 1533.04,611.356 1534.2,611.356 1535.36,611.356 1536.52,611.356 1537.68,611.356 1538.84,611.356 1540,611.356 1541.16,611.356 1542.32,611.356 \n",
       "  1543.48,611.356 1544.64,611.356 1545.8,611.356 1546.96,611.356 1548.12,611.355 1549.28,611.355 1550.44,611.355 1551.6,611.355 1552.76,611.355 1553.92,611.354 \n",
       "  1555.07,611.354 1556.23,611.353 1557.39,611.353 1558.55,611.352 1559.71,611.351 1560.87,611.351 1562.03,611.35 1563.19,611.349 1564.35,611.349 1565.51,611.348 \n",
       "  1566.67,611.347 1567.83,611.347 1568.99,611.347 1570.15,611.347 1571.31,611.347 1572.47,611.347 1573.63,611.347 1574.79,611.347 1575.95,611.347 1577.11,611.347 \n",
       "  1578.27,611.346 1579.43,611.345 1580.59,611.343 1581.75,611.342 1582.9,611.34 1584.06,611.337 1585.22,611.333 1586.38,611.329 1587.54,611.324 1588.7,611.318 \n",
       "  1589.86,611.312 1591.02,611.306 1592.18,611.298 1593.34,611.289 1594.5,611.279 1595.66,611.274 1596.82,611.269 1597.98,611.263 1599.14,611.257 1600.3,611.251 \n",
       "  1601.46,611.249 1602.62,611.247 1603.78,611.244 1604.94,611.242 1606.1,611.24 1607.26,611.241 1608.42,611.243 1609.57,611.244 1610.73,611.246 1611.89,611.247 \n",
       "  1613.05,611.247 1614.21,611.248 1615.37,611.248 1616.53,611.248 1617.69,611.248 1618.85,611.25 1620.01,611.253 1621.17,611.255 1622.33,611.257 1623.49,611.259 \n",
       "  1624.65,611.259 1625.81,611.259 1626.97,611.259 1628.13,611.259 1629.29,611.259 1630.45,611.257 1631.61,611.254 1632.77,611.252 1633.93,611.249 1635.09,611.246 \n",
       "  1636.24,611.233 1637.4,611.219 1638.56,611.203 1639.72,611.185 1640.88,611.165 1642.04,611.134 1643.2,611.098 1644.36,611.057 1645.52,611.01 1646.68,610.956 \n",
       "  1647.84,610.889 1649,610.812 1650.16,610.724 1651.32,610.623 1652.48,610.507 1653.64,610.383 1654.8,610.241 1655.96,610.082 1657.12,609.901 1658.28,609.697 \n",
       "  1659.44,609.451 1660.6,609.171 1661.76,608.855 1662.92,608.497 1664.07,608.095 1665.23,607.727 1666.39,607.321 1667.55,606.875 1668.71,606.384 1669.87,605.844 \n",
       "  1671.03,605.302 1672.19,604.712 1673.35,604.07 1674.51,603.372 1675.67,602.615 1676.83,601.943 1677.99,601.224 1679.15,600.456 1680.31,599.637 1681.47,598.763 \n",
       "  1682.63,598.134 1683.79,597.48 1684.95,596.797 1686.11,596.087 1687.27,595.348 1688.43,594.758 1689.59,594.15 1690.74,593.523 1691.9,592.877 1693.06,592.211 \n",
       "  1694.22,591.874 1695.38,591.531 1696.54,591.183 1697.7,590.83 1698.86,590.471 1700.02,590.251 1701.18,590.029 1702.34,589.803 1703.5,589.574 1704.66,589.342 \n",
       "  1705.82,589.036 1706.98,588.727 1708.14,588.414 1709.3,588.098 1710.46,587.778 1711.62,587.291 1712.78,586.795 1713.94,586.291 1715.1,585.779 1716.26,585.258 \n",
       "  1717.41,584.728 1718.57,584.189 1719.73,583.642 1720.89,583.085 1722.05,582.519 1723.21,581.944 1724.37,581.36 1725.53,580.766 1726.69,580.162 1727.85,579.549 \n",
       "  1729.01,578.627 1730.17,577.684 1731.33,576.72 1732.49,575.733 1733.65,574.725 1734.81,573.795 1735.97,572.846 1737.13,571.879 1738.29,570.891 1739.45,569.885 \n",
       "  1740.61,569.479 1741.77,569.069 1742.93,568.653 1744.09,568.233 1745.24,567.807 1746.4,567.376 1747.56,566.94 1748.72,566.499 1749.88,566.052 1751.04,565.6 \n",
       "  1752.2,564.099 1753.36,562.56 1754.52,560.984 1755.68,559.37 1756.84,557.717 1758,556.138 1759.16,554.525 1760.32,552.876 1761.48,551.19 1762.64,549.468 \n",
       "  1763.8,549.816 1764.96,550.161 1766.12,550.506 1767.28,550.849 1768.44,551.19 1769.6,552.657 1770.76,554.097 1771.91,555.511 1773.07,556.898 1774.23,558.26 \n",
       "  1775.39,558.879 1776.55,559.492 1777.71,560.1 1778.87,560.702 1780.03,561.298 1781.19,560.1 1782.35,558.879 1783.51,557.636 1784.67,556.37 1785.83,555.081 \n",
       "  1786.99,550.388 1788.15,545.405 1789.31,540.124 1790.47,534.537 1791.63,528.639 1792.79,520.127 1793.95,511.023 1795.11,501.32 1796.27,491.018 1797.43,480.122 \n",
       "  1798.58,477.036 1799.74,473.91 1800.9,470.744 1802.06,467.541 1803.22,464.299 1804.38,464.421 1805.54,464.542 1806.7,464.662 1807.86,464.781 1809.02,464.898 \n",
       "  1810.18,467.4 1811.34,469.878 1812.5,472.33 1813.66,474.756 1814.82,477.157 1815.98,479.061 1817.14,480.951 1818.3,482.825 1819.46,484.683 1820.62,486.526 \n",
       "  1821.78,485.26 1822.94,483.987 1824.1,482.706 1825.26,481.418 1826.41,480.122 1827.57,477.873 1828.73,475.596 1829.89,473.291 1831.05,470.957 1832.21,468.595 \n",
       "  1833.37,464.724 1834.53,460.798 1835.69,456.819 1836.85,452.787 1838.01,448.704 1839.17,444.679 1840.33,440.602 1841.49,436.475 1842.65,432.298 1843.81,428.073 \n",
       "  1844.97,420.206 1846.13,412.19 1847.29,404.034 1848.45,395.747 1849.61,387.341 1850.77,378.827 1851.93,370.216 1853.08,361.524 1854.24,352.762 1855.4,343.945 \n",
       "  1856.56,338.294 1857.72,332.645 1858.88,327 1860.04,321.366 1861.2,315.747 1862.36,311.722 1863.52,307.691 1864.68,303.656 1865.84,299.618 1867,295.581 \n",
       "  1868.16,292.417 1869.32,289.271 1870.48,286.142 1871.64,283.032 1872.8,279.942 1873.96,274.471 1875.12,269.04 1876.28,263.653 1877.44,258.316 1878.6,253.034 \n",
       "  1879.75,244.963 1880.91,237.085 1882.07,229.416 1883.23,221.977 1884.39,214.785 1885.55,206.864 1886.71,199.224 1887.87,191.891 1889.03,184.887 1890.19,178.235 \n",
       "  1891.35,174.384 1892.51,170.729 1893.67,167.277 1894.83,164.031 1895.99,160.996 1897.15,159.424 1898.31,157.903 1899.47,156.432 1900.63,155.013 1901.79,153.646 \n",
       "  1902.95,155.442 1904.11,157.366 1905.27,159.416 1906.43,161.591 1907.58,163.89 1908.74,169.799 1909.9,176.336 1911.06,183.475 1912.22,191.186 1913.38,199.436 \n",
       "  1914.54,208.626 1915.7,218.197 1916.86,228.109 1918.02,238.324 1919.18,248.801 1920.34,258.652 1921.5,268.688 1922.66,278.877 1923.82,289.188 1924.98,299.591 \n",
       "  1926.14,302.806 1927.3,306.025 1928.46,309.249 1929.62,312.476 1930.78,315.706 1931.94,313.273 1933.1,310.836 1934.25,308.395 1935.41,305.951 1936.57,303.504 \n",
       "  1937.73,297.9 1938.89,292.344 1940.05,286.843 1941.21,281.403 1942.37,276.03 1943.53,265.266 1944.69,254.728 1945.85,244.455 1947.01,234.485 1948.17,224.858 \n",
       "  1949.33,212.822 1950.49,201.437 1951.65,190.778 1952.81,180.919 1953.97,171.927 1955.13,162.771 1956.29,154.817 1957.45,148.141 1958.61,142.808 1959.77,138.872 \n",
       "  1960.93,136.743 1962.08,135.938 1963.24,136.463 1964.4,138.314 1965.56,141.476 1966.72,142.743 1967.88,144.137 1969.04,145.657 1970.2,147.302 1971.36,149.069 \n",
       "  1972.52,151.616 1973.68,154.375 1974.84,157.344 1976,160.517 1977.16,163.89 1978.32,168.617 1979.48,173.625 1980.64,178.901 1981.8,184.434 1982.96,190.209 \n",
       "  1984.12,197.201 1985.28,204.53 1986.44,212.172 1987.6,220.105 1988.75,228.306 1989.91,236.621 1991.07,245.187 1992.23,253.978 1993.39,262.97 1994.55,272.138 \n",
       "  1995.71,281.457 1996.87,290.902 1998.03,300.448 1999.19,310.07 2000.35,319.745 2001.51,327.831 2002.67,335.927 2003.83,344.018 2004.99,352.093 2006.15,360.138 \n",
       "  2007.31,365.668 2008.47,371.157 2009.63,376.601 2010.79,381.996 2011.95,387.341 2013.11,391.94 2014.27,396.506 2015.42,401.035 2016.58,405.527 2017.74,409.979 \n",
       "  2018.9,407.841 2020.06,405.689 2021.22,403.523 2022.38,401.343 2023.54,399.149 2024.7,399.002 2025.86,398.851 2027.02,398.698 2028.18,398.542 2029.34,398.383 \n",
       "  2030.5,404.934 2031.66,411.374 2032.82,417.698 2033.98,423.903 2035.14,429.986 2036.3,435.381 2037.46,440.684 2038.62,445.892 2039.78,451.004 2040.94,456.019 \n",
       "  2042.1,463.427 2043.25,470.613 2044.41,477.576 2045.57,484.312 2046.73,490.82 2047.89,497.626 2049.05,504.163 2050.21,510.433 2051.37,516.437 2052.53,522.179 \n",
       "  2053.69,527.237 2054.85,532.077 2056.01,536.703 2057.17,541.12 2058.33,545.331 2059.49,549.65 2060.65,553.759 2061.81,557.663 2062.97,561.367 2064.13,564.874 \n",
       "  2065.29,567.805 2066.45,570.588 2067.61,573.227 2068.77,575.728 2069.92,578.095 2071.08,579.017 2072.24,579.916 2073.4,580.792 2074.56,581.645 2075.72,582.476 \n",
       "  2076.88,583.467 2078.04,584.426 2079.2,585.356 2080.36,586.256 2081.52,587.128 2082.68,588.379 2083.84,589.575 2085,590.718 2086.16,591.811 2087.32,592.855 \n",
       "  2088.48,593.729 2089.64,594.568 2090.8,595.373 2091.96,596.144 2093.12,596.884 2094.28,597.493 2095.44,598.081 2096.59,598.646 2097.75,599.191 2098.91,599.716 \n",
       "  2100.07,600.138 2101.23,600.546 2102.39,600.942 2103.55,601.325 2104.71,601.696 2105.87,602.055 2107.03,602.402 2108.19,602.738 2109.35,603.062 2110.51,603.376 \n",
       "  2111.67,603.56 2112.83,603.739 2113.99,603.915 2115.15,604.088 2116.31,604.257 2117.47,604.411 2118.63,604.562 2119.79,604.71 2120.95,604.855 2122.11,604.998 \n",
       "  2123.27,605.037 2124.42,605.076 2125.58,605.114 2126.74,605.152 2127.9,605.189 2129.06,605.076 2130.22,604.961 2131.38,604.843 2132.54,604.723 2133.7,604.6 \n",
       "  2134.86,604.04 2136.02,603.44 2137.18,602.797 2138.34,602.108 2139.5,601.372 2140.66,600.827 2141.82,600.256 2142.98,599.658 2144.14,599.033 2145.3,598.379 \n",
       "  2146.46,598.187 2147.62,597.992 2148.78,597.795 2149.94,597.596 2151.09,597.393 2152.25,597.596 2153.41,597.795 2154.57,597.992 2155.73,598.187 2156.89,598.379 \n",
       "  2158.05,598.941 2159.21,599.482 2160.37,600.003 2161.53,600.504 2162.69,600.985 2163.85,601.396 2165.01,601.792 2166.17,602.174 2167.33,602.542 2168.49,602.896 \n",
       "  2169.65,602.393 2170.81,601.862 2171.97,601.303 2173.13,600.714 2174.29,600.094 2175.45,599.756 2176.61,599.406 2177.76,599.044 2178.92,598.669 2180.08,598.281 \n",
       "  2181.24,598.572 2182.4,598.857 2183.56,599.137 2184.72,599.412 2185.88,599.681 2187.04,600.373 2188.2,601.03 2189.36,601.652 2190.52,602.241 2191.68,602.798 \n",
       "  2192.84,602.523 2194,602.241 2195.16,601.95 2196.32,601.652 2197.48,601.345 2198.64,600.623 2199.8,599.857 2200.96,599.044 2202.12,598.182 2203.28,597.269 \n",
       "  2204.44,597.53 2205.59,597.785 2206.75,598.036 2207.91,598.282 2209.07,598.523 2210.23,599.41 2211.39,600.244 2212.55,601.028 2213.71,601.763 2214.87,602.453 \n",
       "  2216.03,603.227 2217.19,603.94 2218.35,604.597 2219.51,605.2 2220.67,605.754 2221.83,606.389 2222.99,606.958 2224.15,607.467 2225.31,607.922 2226.47,608.328 \n",
       "  2227.63,608.682 2228.79,608.998 2229.95,609.28 2231.11,609.531 2232.26,609.754 2233.42,609.978 2234.58,610.174 2235.74,610.343 2236.9,610.49 2238.06,610.617 \n",
       "  2239.22,610.74 2240.38,610.843 2241.54,610.93 2242.7,611.003 2243.86,611.064 2245.02,611.114 2246.18,611.155 2247.34,611.189 2248.5,611.218 2249.66,611.242 \n",
       "  2250.82,611.257 2251.98,611.269 2253.14,611.281 2254.3,611.29 2255.46,611.299 2256.62,611.305 2257.78,611.311 2258.93,611.316 2260.09,611.321 2261.25,611.325 \n",
       "  2262.41,611.329 2263.57,611.332 2264.73,611.335 2265.89,611.338 2267.05,611.34 2268.21,611.342 2269.37,611.343 2270.53,611.345 2271.69,611.346 2272.85,611.347 \n",
       "  2274.01,611.348 2275.17,611.349 2276.33,611.35 2277.49,611.35 2278.65,611.351 2279.81,611.351 2280.97,611.352 2282.13,611.352 2283.29,611.353 2284.45,611.353 \n",
       "  2285.61,611.353 2286.76,611.353 2287.92,611.354 2289.08,611.354 2290.24,611.354 2291.4,611.354 2292.56,611.354 2293.72,611.354 2294.88,611.354 2296.04,611.354 \n",
       "  2297.2,611.354 2298.36,611.354 2299.52,611.354 2300.68,611.354 2301.84,611.354 2303,611.354 2304.16,611.354 2305.32,611.354 2306.48,611.354 2307.64,611.354 \n",
       "  2308.8,611.354 2309.96,611.354 2311.12,611.354 2312.28,611.354 2313.43,611.354 2314.59,611.354 2315.75,611.353 2316.91,611.353 2318.07,611.353 2319.23,611.353 \n",
       "  2320.39,611.353 2321.55,611.353 2322.71,611.353 2323.87,611.353 2325.03,611.353 2326.19,611.353 2327.35,611.353 2328.51,611.354 \n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 510.138, 1479.62)\" x=\"510.138\" y=\"1479.62\">7900</text>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 645.746, 1479.62)\" x=\"645.746\" y=\"1479.62\">8000</text>\n",
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       "<g clip-path=\"url(#clip3600)\">\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 272.041, 1052.99)\" x=\"272.041\" y=\"1052.99\">0.006</text>\n",
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       "  320.288,1411.36 321.644,1411.36 323,1411.36 324.356,1411.36 325.712,1411.36 327.068,1411.36 328.424,1411.36 329.78,1411.36 331.136,1411.36 332.492,1411.36 \n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2158.12, 1479.62)\" x=\"2158.12\" y=\"1479.62\">8500</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2308.91, 1479.62)\" x=\"2308.91\" y=\"1479.62\">8600</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1472.04, 1428.86)\" x=\"1472.04\" y=\"1428.86\">0.0000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1472.04, 1329.25)\" x=\"1472.04\" y=\"1329.25\">0.0025</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1472.04, 1229.64)\" x=\"1472.04\" y=\"1229.64\">0.0050</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1472.04, 1130.03)\" x=\"1472.04\" y=\"1130.03\">0.0075</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 1472.04, 1030.42)\" x=\"1472.04\" y=\"1030.42\">0.0100</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:84px; text-anchor:middle;\" transform=\"rotate(0, 1924.4, 873.2)\" x=\"1924.4\" y=\"873.2\">Sample 4</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1924.4, 1559.48)\" x=\"1924.4\" y=\"1559.48\">Calendar Age</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip3600)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 1289.29, 1173.65)\" x=\"1289.29\" y=\"1173.65\">Likelihood</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip3605)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1520.29,1411.32 1521.8,1411.32 1523.3,1411.32 1524.81,1411.32 1526.32,1411.33 1527.83,1411.33 1529.34,1411.33 1530.84,1411.33 1532.35,1411.33 1533.86,1411.34 \n",
       "  1535.37,1411.34 1536.87,1411.34 1538.38,1411.34 1539.89,1411.35 1541.4,1411.35 1542.91,1411.35 1544.41,1411.35 1545.92,1411.35 1547.43,1411.35 1548.94,1411.35 \n",
       "  1550.45,1411.35 1551.95,1411.35 1553.46,1411.35 1554.97,1411.35 1556.48,1411.35 1557.98,1411.35 1559.49,1411.35 1561,1411.35 1562.51,1411.35 1564.02,1411.35 \n",
       "  1565.52,1411.35 1567.03,1411.35 1568.54,1411.35 1570.05,1411.35 1571.56,1411.35 1573.06,1411.35 1574.57,1411.35 1576.08,1411.35 1577.59,1411.35 1579.09,1411.35 \n",
       "  1580.6,1411.35 1582.11,1411.35 1583.62,1411.35 1585.13,1411.35 1586.63,1411.35 1588.14,1411.35 1589.65,1411.35 1591.16,1411.35 1592.67,1411.35 1594.17,1411.35 \n",
       "  1595.68,1411.35 1597.19,1411.35 1598.7,1411.35 1600.21,1411.35 1601.71,1411.35 1603.22,1411.35 1604.73,1411.35 1606.24,1411.35 1607.74,1411.35 1609.25,1411.35 \n",
       "  1610.76,1411.35 1612.27,1411.35 1613.78,1411.35 1615.28,1411.35 1616.79,1411.35 1618.3,1411.35 1619.81,1411.35 1621.32,1411.35 1622.82,1411.35 1624.33,1411.35 \n",
       "  1625.84,1411.35 1627.35,1411.35 1628.85,1411.35 1630.36,1411.35 1631.87,1411.35 1633.38,1411.35 1634.89,1411.35 1636.39,1411.35 1637.9,1411.35 1639.41,1411.35 \n",
       "  1640.92,1411.35 1642.43,1411.35 1643.93,1411.34 1645.44,1411.34 1646.95,1411.33 1648.46,1411.33 1649.97,1411.32 1651.47,1411.31 1652.98,1411.29 1654.49,1411.28 \n",
       "  1656,1411.26 1657.5,1411.23 1659.01,1411.21 1660.52,1411.17 1662.03,1411.12 1663.54,1411.06 1665.04,1410.98 1666.55,1410.89 1668.06,1410.77 1669.57,1410.6 \n",
       "  1671.08,1410.4 1672.58,1410.14 1674.09,1409.82 1675.6,1409.43 1677.11,1408.92 1678.61,1408.29 1680.12,1407.51 1681.63,1406.58 1683.14,1405.44 1684.65,1404.61 \n",
       "  1686.15,1403.67 1687.66,1402.61 1689.17,1401.44 1690.68,1400.13 1692.19,1399.14 1693.69,1398.08 1695.2,1396.94 1696.71,1395.71 1698.22,1394.38 1699.72,1392.48 \n",
       "  1701.23,1390.4 1702.74,1388.12 1704.25,1385.65 1705.76,1382.96 1707.26,1380.59 1708.77,1378.07 1710.28,1375.37 1711.79,1372.51 1713.3,1369.46 1714.8,1366.6 \n",
       "  1716.31,1363.59 1717.82,1360.42 1719.33,1357.09 1720.84,1353.59 1722.34,1350.16 1723.85,1346.56 1725.36,1342.78 1726.87,1338.84 1728.37,1334.71 1729.88,1331.66 \n",
       "  1731.39,1328.52 1732.9,1325.31 1734.41,1322.02 1735.91,1318.65 1737.42,1316.74 1738.93,1314.8 1740.44,1312.84 1741.95,1310.85 1743.45,1308.84 1744.96,1309.51 \n",
       "  1746.47,1310.19 1747.98,1310.85 1749.48,1311.52 1750.99,1312.18 1752.5,1313.1 1754.01,1314 1755.52,1314.91 1757.02,1315.8 1758.53,1316.69 1760.04,1318.62 \n",
       "  1761.55,1320.51 1763.06,1322.38 1764.56,1324.22 1766.07,1326.04 1767.58,1329.24 1769.09,1332.36 1770.6,1335.4 1772.1,1338.37 1773.61,1341.25 1775.12,1340.72 \n",
       "  1776.63,1340.19 1778.13,1339.66 1779.64,1339.13 1781.15,1338.59 1782.66,1337.72 1784.17,1336.84 1785.67,1335.95 1787.18,1335.05 1788.69,1334.13 1790.2,1338.03 \n",
       "  1791.71,1341.78 1793.21,1345.39 1794.72,1348.85 1796.23,1352.18 1797.74,1357.81 1799.24,1363 1800.75,1367.78 1802.26,1372.16 1803.77,1376.17 1805.28,1378.27 \n",
       "  1806.78,1380.26 1808.29,1382.16 1809.8,1383.96 1811.31,1385.67 1812.82,1385.43 1814.32,1385.19 1815.83,1384.95 1817.34,1384.7 1818.85,1384.46 1820.36,1383.2 \n",
       "  1821.86,1381.9 1823.37,1380.54 1824.88,1379.14 1826.39,1377.68 1827.89,1376.62 1829.4,1375.53 1830.91,1374.42 1832.42,1373.28 1833.93,1372.11 1835.43,1370.94 \n",
       "  1836.94,1369.74 1838.45,1368.5 1839.96,1367.23 1841.47,1365.93 1842.97,1364.2 1844.48,1362.42 1845.99,1360.57 1847.5,1358.66 1849,1356.69 1850.51,1354.28 \n",
       "  1852.02,1351.78 1853.53,1349.21 1855.04,1346.56 1856.54,1343.84 1858.05,1340.28 1859.56,1336.6 1861.07,1332.8 1862.58,1328.87 1864.08,1324.82 1865.59,1323.25 \n",
       "  1867.1,1321.65 1868.61,1320.03 1870.11,1318.37 1871.62,1316.69 1873.13,1314.33 1874.64,1311.91 1876.15,1309.45 1877.65,1306.93 1879.16,1304.36 1880.67,1299.34 \n",
       "  1882.18,1294.16 1883.69,1288.84 1885.19,1283.36 1886.7,1277.74 1888.21,1271.13 1889.72,1264.33 1891.23,1257.35 1892.73,1250.19 1894.24,1242.86 1895.75,1232.68 \n",
       "  1897.26,1222.18 1898.76,1211.37 1900.27,1200.27 1901.78,1188.9 1903.29,1184.66 1904.8,1180.4 1906.3,1176.11 1907.81,1171.8 1909.32,1167.46 1910.83,1162.02 \n",
       "  1912.34,1156.55 1913.84,1151.06 1915.35,1145.55 1916.86,1140.02 1918.37,1124.49 1919.87,1108.94 1921.38,1093.49 1922.89,1078.21 1924.4,1063.21 1925.91,1051.52 \n",
       "  1927.41,1040.07 1928.92,1028.9 1930.43,1018.05 1931.94,1007.6 1933.45,1005.79 1934.95,1004 1936.46,1002.23 1937.97,1000.47 1939.48,998.73 1940.99,997.866 \n",
       "  1942.49,997.007 1944,996.153 1945.51,995.302 1947.02,994.457 1948.52,985.461 1950.03,977.059 1951.54,969.293 1953.05,962.205 1954.56,955.829 1956.06,954.104 \n",
       "  1957.57,952.496 1959.08,951.005 1960.59,949.633 1962.1,948.38 1963.6,944.244 1965.11,940.916 1966.62,938.414 1968.13,936.752 1969.63,935.938 1971.14,936.202 \n",
       "  1972.65,938.049 1974.16,941.46 1975.67,946.401 1977.17,952.824 1978.68,959.964 1980.19,968.078 1981.7,977.103 1983.21,986.969 1984.71,997.603 1986.22,1009.5 \n",
       "  1987.73,1022.18 1989.24,1035.54 1990.75,1049.49 1992.25,1063.92 1993.76,1076.48 1995.27,1089.33 1996.78,1102.39 1998.28,1115.62 1999.79,1128.93 2001.3,1132.26 \n",
       "  2002.81,1135.59 2004.32,1138.91 2005.82,1142.23 2007.33,1145.55 2008.84,1160.93 2010.35,1176.11 2011.86,1191.01 2013.36,1205.56 2014.87,1219.71 2016.38,1232.27 \n",
       "  2017.89,1244.37 2019.39,1256 2020.9,1267.12 2022.41,1277.74 2023.92,1289.84 2025.43,1301.25 2026.93,1311.96 2028.44,1321.96 2029.95,1331.26 2031.46,1339.12 \n",
       "  2032.97,1346.39 2034.47,1353.1 2035.98,1359.27 2037.49,1364.92 2039,1368.83 2040.5,1372.47 2042.01,1375.87 2043.52,1379.02 2045.03,1381.95 2046.54,1385.76 \n",
       "  2048.04,1389.12 2049.55,1392.09 2051.06,1394.7 2052.57,1396.99 2054.08,1397.19 2055.58,1397.38 2057.09,1397.56 2058.6,1397.75 2060.11,1397.93 2061.62,1397.93 \n",
       "  2063.12,1397.93 2064.63,1397.93 2066.14,1397.93 2067.65,1397.93 2069.15,1398.29 2070.66,1398.65 2072.17,1398.99 2073.68,1399.33 2075.19,1399.66 2076.69,1400.6 \n",
       "  2078.2,1401.48 2079.71,1402.29 2081.22,1403.04 2082.73,1403.74 2084.23,1404.84 2085.74,1405.79 2087.25,1406.62 2088.76,1407.34 2090.26,1407.96 2091.77,1408.22 \n",
       "  2093.28,1408.47 2094.79,1408.71 2096.3,1408.92 2097.8,1409.12 2099.31,1409.23 2100.82,1409.33 2102.33,1409.42 2103.84,1409.51 2105.34,1409.6 2106.85,1409.45 \n",
       "  2108.36,1409.28 2109.87,1409.1 2111.38,1408.9 2112.88,1408.69 2114.39,1408.72 2115.9,1408.76 2117.41,1408.79 2118.91,1408.82 2120.42,1408.85 2121.93,1409.06 \n",
       "  2123.44,1409.25 2124.95,1409.43 2126.45,1409.6 2127.96,1409.75 2129.47,1409.92 2130.98,1410.08 2132.49,1410.22 2133.99,1410.35 2135.5,1410.46 2137.01,1410.42 \n",
       "  2138.52,1410.37 2140.02,1410.31 2141.53,1410.26 2143.04,1410.2 2144.55,1410.05 2146.06,1409.89 2147.56,1409.71 2149.07,1409.5 2150.58,1409.28 2152.09,1409.11 \n",
       "  2153.6,1408.93 2155.1,1408.74 2156.61,1408.53 2158.12,1408.31 2159.63,1408.3 2161.14,1408.29 2162.64,1408.28 2164.15,1408.27 2165.66,1408.26 2167.17,1408.39 \n",
       "  2168.67,1408.51 2170.18,1408.63 2171.69,1408.74 2173.2,1408.85 2174.71,1408.98 2176.21,1409.1 2177.72,1409.21 2179.23,1409.32 2180.74,1409.42 2182.25,1409.63 \n",
       "  2183.75,1409.81 2185.26,1409.98 2186.77,1410.14 2188.28,1410.27 2189.78,1410.38 2191.29,1410.48 2192.8,1410.57 2194.31,1410.65 2195.82,1410.73 2197.32,1410.66 \n",
       "  2198.83,1410.59 2200.34,1410.51 2201.85,1410.43 2203.36,1410.33 2204.86,1410.28 2206.37,1410.22 2207.88,1410.16 2209.39,1410.09 2210.89,1410.02 2212.4,1410.25 \n",
       "  2213.91,1410.44 2215.42,1410.6 2216.93,1410.73 2218.43,1410.85 2219.94,1410.99 2221.45,1411.1 2222.96,1411.17 2224.47,1411.23 2225.97,1411.27 2227.48,1411.28 \n",
       "  2228.99,1411.3 2230.5,1411.31 2232.01,1411.32 2233.51,1411.33 2235.02,1411.33 2236.53,1411.33 2238.04,1411.34 2239.54,1411.34 2241.05,1411.34 2242.56,1411.34 \n",
       "  2244.07,1411.34 2245.58,1411.34 2247.08,1411.34 2248.59,1411.34 2250.1,1411.34 2251.61,1411.34 2253.12,1411.34 2254.62,1411.35 2256.13,1411.35 2257.64,1411.35 \n",
       "  2259.15,1411.35 2260.65,1411.34 2262.16,1411.34 2263.67,1411.34 2265.18,1411.34 2266.69,1411.34 2268.19,1411.34 2269.7,1411.34 2271.21,1411.34 2272.72,1411.34 \n",
       "  2274.23,1411.34 2275.73,1411.35 2277.24,1411.35 2278.75,1411.35 2280.26,1411.35 2281.77,1411.35 2283.27,1411.35 2284.78,1411.35 2286.29,1411.35 2287.8,1411.35 \n",
       "  2289.3,1411.35 2290.81,1411.35 2292.32,1411.35 2293.83,1411.35 2295.34,1411.35 2296.84,1411.36 2298.35,1411.36 2299.86,1411.36 2301.37,1411.36 2302.88,1411.36 \n",
       "  2304.38,1411.36 2305.89,1411.36 2307.4,1411.36 2308.91,1411.36 2310.41,1411.36 2311.92,1411.36 2313.43,1411.36 2314.94,1411.36 2316.45,1411.36 2317.95,1411.36 \n",
       "  2319.46,1411.36 2320.97,1411.36 2322.48,1411.36 2323.99,1411.36 2325.49,1411.36 2327,1411.36 2328.51,1411.36 \n",
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smpl.Params = fill(NaN, length(intcal13[\"Age_Calendar\"]), nSamples)\n",
    "hdl = plot(layout=nSamples)\n",
    "for i = 1:nSamples\n",
    "    # The likelihood that a measured 14C age could result from a sample of\n",
    "    # a given calendar age is proportional to the intergral of the product\n",
    "    # of the two respective distributions\n",
    "    likelihood = normproduct.(smpl.Age_14C[i], smpl.Age_14C_sigma[i], intcal13[\"Age_14C\"], intcal13[\"Age_sigma\"])\n",
    "    likelihood ./= sum(likelihood) * intcal13[\"dt\"] # Normalize\n",
    "\n",
    "    # Estimate mean and standard deviation by drawing samples from distribution\n",
    "    samples = draw_from_distribution(likelihood, 10^6) .* maximum(intcal13[\"Age_Calendar\"])\n",
    "    smpl.Age[i] = mean(samples)\n",
    "    smpl.Age_sigma[i] = std(samples)\n",
    "    smpl.Age_025CI[i] = percentile(samples,2.5)\n",
    "    smpl.Age_975CI[i] = percentile(samples,97.5)\n",
    "\n",
    "    # Populate smpl.Params with log likelihood for each sample\n",
    "    smpl.Params[:,i] = normproduct_ll.(smpl.Age_14C[i], smpl.Age_14C_sigma[i], intcal13[\"Age_14C\"], intcal13[\"Age_sigma\"])\n",
    "\n",
    "    # Plot likelihood vector for each sample\n",
    "    t = (intcal13[\"Age_Calendar\"] .> smpl.Age[i] - 5*smpl.Age_sigma[i]) .& (intcal13[\"Age_Calendar\"] .< smpl.Age[i] + 5*smpl.Age_sigma[i])\n",
    "    plot!(hdl[i], intcal13[\"Age_Calendar\"][t], likelihood[t], label=\"\", xlabel=\"Calendar Age\", ylabel=\"Likelihood\", title=\"$(smpl.Name[i])\")\n",
    "end\n",
    "display(hdl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Configure and run stratigraphic model\n",
    "note: to spare Binder's servers, this demo uses\n",
    "```\n",
    "config.nsteps = 3000 \n",
    "config.burnin = 2000*npoints_approx\n",
    "```\n",
    "However, you probably want higher numbers for a publication-quality result, for instance \n",
    "```\n",
    "config.nsteps = 30000 # Number of steps to run in distribution MCMC\n",
    "config.burnin = 10000*npoints_approx # Number to discard\n",
    "```\n",
    "and examine the log likelihood plot to make sure you've converged.\n",
    "\n",
    "To run the stratigraphic MCMC model, we call the `StratMetropolis14C` function. If you're not using radiocarbon ages and want to run stratigraphic model with Gaussian mean age and standard deviation for some number of stratigraphic horizons, then you can set `smpl.Age` and `smpl.Age_sigma` directly, but then you'll need to call `StratMetropolis` instead of `StratMetropolis14C`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating stratigraphic age-depth model...\n",
      "Burn-in: 680000 steps\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBurn-in...100%|█████████████████████████████████████████| Time: 0:12:54\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting sieved stationary distribution: 1020000 steps\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mCollecting...100%|██████████████████████████████████████| Time: 0:18:54\u001b[39m\n"
     ]
    },
    {
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       "  581.163,778.131 581.839,503.5 582.516,602.68 583.192,657.163 583.868,590.558 584.545,303.01 585.221,447.3 585.898,307.651 586.574,365.869 587.251,413.071 \n",
       "  587.927,571.129 588.604,431.239 589.28,618.297 589.956,444.485 590.633,555.588 591.309,195.549 591.986,390.254 592.662,413.401 593.339,152.331 594.015,371.342 \n",
       "  594.692,594.289 595.368,568.11 596.045,431.641 596.721,356.376 597.397,790.911 598.074,891.703 598.75,627.455 599.427,347.619 600.103,438.345 600.78,349.076 \n",
       "  601.456,419.562 602.133,238.337 602.809,355.918 603.485,330.988 604.162,401.467 604.838,482.442 605.515,305.439 606.191,448.975 606.868,462.689 607.544,383.146 \n",
       "  608.221,340.045 608.897,523.703 609.573,330.89 610.25,530.442 610.926,252.84 611.603,692.51 612.279,428.59 612.956,415.582 613.632,526.624 614.309,603.546 \n",
       "  614.985,275.213 615.661,305.845 616.338,429.146 617.014,740.194 617.691,408.328 618.367,543.503 619.044,550.583 619.72,436.434 620.397,290.675 621.073,295.63 \n",
       "  621.749,701.934 622.426,588.436 623.102,643.234 623.779,181.767 624.455,435.492 625.132,336.791 625.808,490.035 626.485,398.452 627.161,322.361 627.838,630.734 \n",
       "  628.514,734.68 629.19,496.867 629.867,291.75 630.543,492.985 631.22,589.585 631.896,472.074 632.573,217.554 633.249,356.66 633.926,344.907 634.602,629.855 \n",
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       "  655.572,639.605 656.248,605.206 656.925,468.959 657.601,402.35 658.278,610.962 658.954,516.518 659.63,384.114 660.307,460.117 660.983,410.431 661.66,332.914 \n",
       "  662.336,430.342 663.013,304.759 663.689,470.689 664.366,232.173 665.042,164.674 665.719,324.546 666.395,387.33 667.071,560.324 667.748,426.141 668.424,372.389 \n",
       "  669.101,461.387 669.777,614.346 670.454,522.469 671.13,686.39 671.807,679.857 672.483,615.212 673.159,392.596 673.836,298.922 674.512,277.469 675.189,350.503 \n",
       "  675.865,381.551 676.542,302.806 677.218,163.426 677.895,465.119 678.571,334.829 679.247,316.372 679.924,325.438 680.6,589.592 681.277,459.319 681.953,579.765 \n",
       "  682.63,369.911 683.306,348.024 683.983,584.333 684.659,451.253 685.335,415.225 686.012,577.926 686.688,536.783 687.365,514.688 688.041,379.521 688.718,638.659 \n",
       "  689.394,631.392 690.071,521.14 690.747,487.662 691.423,470.53 692.1,710.839 692.776,637.099 693.453,543.708 694.129,289.382 694.806,533.09 695.482,434.993 \n",
       "  696.159,525.921 696.835,346.142 697.511,329.877 698.188,395.671 698.864,292.097 699.541,317.781 700.217,420.45 700.894,643.98 701.57,425.359 702.247,317.039 \n",
       "  702.923,322.902 703.6,319.623 704.276,243.9 704.952,197.858 705.629,387.419 706.305,488.051 706.982,568.211 707.658,331.313 708.335,552.187 709.011,208.226 \n",
       "  709.688,361.567 710.364,293.743 711.04,532.944 711.717,563.876 712.393,338.4 713.07,390.832 713.746,279.271 714.423,385.02 715.099,468.873 715.776,334.641 \n",
       "  716.452,463.156 717.128,270.732 717.805,379.385 718.481,394.747 719.158,483.109 719.834,467.061 720.511,576.549 721.187,645.289 721.864,582.771 722.54,665.937 \n",
       "  723.216,574.181 723.893,455.574 724.569,415.284 725.246,439.133 725.922,574.675 726.599,411.668 727.275,218.48 727.952,301.005 728.628,504.169 729.304,228.432 \n",
       "  729.981,340.067 730.657,504.626 731.334,314.989 732.01,572.334 732.687,265.865 733.363,565.251 734.04,591.699 734.716,497.511 735.393,420.426 736.069,199.717 \n",
       "  736.745,249.106 737.422,381.66 738.098,619.953 738.775,723.321 739.451,641.755 740.128,600.671 740.804,704.255 741.481,609.257 742.157,667.493 742.833,514.255 \n",
       "  743.51,566.223 744.186,402.99 744.863,885.514 745.539,506.046 746.216,465.907 746.892,673.52 747.569,400.863 748.245,572.902 748.921,491.796 749.598,669.544 \n",
       "  750.274,596.399 750.951,345.055 751.627,495.594 752.304,633.418 752.98,504.684 753.657,566.884 754.333,537.357 755.009,581.403 755.686,573.026 756.362,273.834 \n",
       "  757.039,275.838 757.715,290.718 758.392,285.41 759.068,196.947 759.745,455.989 760.421,582.988 761.097,449.526 761.774,458.468 762.45,503.252 763.127,588.636 \n",
       "  763.803,568.379 764.48,612.351 765.156,953.076 765.833,745.272 766.509,729.299 767.185,838.304 767.862,949.244 768.538,780.989 769.215,566.278 769.891,434.628 \n",
       "  770.568,263.298 771.244,321.483 771.921,332.545 772.597,410.375 773.274,485.881 773.95,618.542 774.626,505.961 775.303,312.999 775.979,283.415 776.656,358.751 \n",
       "  777.332,269.495 778.009,323.067 778.685,466.876 779.362,619.981 780.038,662.174 780.714,411.704 781.391,435.097 782.067,819.214 782.744,435.101 783.42,206.291 \n",
       "  784.097,421.581 784.773,531.059 785.45,358.213 786.126,381.993 786.802,506.429 787.479,318.144 788.155,644.878 788.832,550.666 789.508,217.268 790.185,251.657 \n",
       "  790.861,725.186 791.538,497.672 792.214,822.127 792.89,438.877 793.567,461.291 794.243,389.787 794.92,778.964 795.596,390.536 796.273,588.726 796.949,639.831 \n",
       "  797.626,308.721 798.302,466.866 798.978,243.368 799.655,257.963 800.331,541.091 801.008,347.643 801.684,378.478 802.361,603.411 803.037,444.406 803.714,332.17 \n",
       "  804.39,298.779 805.066,333.397 805.743,411.553 806.419,346.02 807.096,353.402 807.772,444.044 808.449,233.352 809.125,666.049 809.802,483.845 810.478,379.329 \n",
       "  811.155,224.251 811.831,463.893 812.507,656.855 813.184,331.291 813.86,460.244 814.537,377.956 815.213,688.926 815.89,298.086 816.566,551.512 817.243,366.695 \n",
       "  817.919,290.586 818.595,208.215 819.272,193.384 819.948,268.91 820.625,593.381 821.301,665.852 821.978,614.306 822.654,526.1 823.331,680.946 824.007,399.48 \n",
       "  824.683,321.409 825.36,468.891 826.036,418.548 826.713,475.946 827.389,485.232 828.066,359.217 828.742,271.464 829.419,514.147 830.095,495.066 830.771,379.96 \n",
       "  831.448,442.227 832.124,283.856 832.801,418.02 833.477,330.589 834.154,622.992 834.83,577.317 835.507,798.429 836.183,556.446 836.859,628.565 837.536,554.546 \n",
       "  838.212,544.991 838.889,268.029 839.565,708.99 840.242,554.664 840.918,506.724 841.595,486.133 842.271,464.926 842.948,559.146 843.624,633.258 844.3,304.429 \n",
       "  844.977,584.75 845.653,171.787 846.33,594.796 847.006,569.477 847.683,353.478 848.359,196.839 849.036,193.141 849.712,291.092 850.388,466.854 851.065,294.567 \n",
       "  851.741,288.971 852.418,264.788 853.094,346.151 853.771,423.436 854.447,415.263 855.124,382.785 855.8,314.969 856.476,393.203 857.153,402.429 857.829,412.978 \n",
       "  858.506,632.61 859.182,605.642 859.859,602.478 860.535,584.969 861.212,530.083 861.888,365.568 862.564,455.838 863.241,498.19 863.917,411.088 864.594,535.918 \n",
       "  865.27,232.847 865.947,219.887 866.623,359.126 867.3,248.517 867.976,305.394 868.652,662.514 869.329,656.923 870.005,460.885 870.682,417.869 871.358,349.856 \n",
       "  872.035,397.227 872.711,485.128 873.388,522.543 874.064,456.75 874.74,336.114 875.417,573.054 876.093,614.762 876.77,551.877 877.446,196.35 878.123,456.137 \n",
       "  878.799,527.163 879.476,414.433 880.152,657.625 880.829,456.832 881.505,485.311 882.181,320.133 882.858,321.386 883.534,506.984 884.211,445.715 884.887,466.964 \n",
       "  885.564,476.891 886.24,639.874 886.917,862.672 887.593,588.088 888.269,527.956 888.946,457.068 889.622,361.116 890.299,255.688 890.975,248.26 891.652,707.681 \n",
       "  892.328,371.923 893.005,570.607 893.681,568.907 894.357,388.387 895.034,463.74 895.71,529.198 896.387,538.892 897.063,555.618 897.74,440.36 898.416,494.862 \n",
       "  899.093,446.651 899.769,343.46 900.445,461.303 901.122,462.157 901.798,460.196 902.475,286.334 903.151,600.411 903.828,389.1 904.504,547.513 905.181,535.284 \n",
       "  905.857,484.625 906.533,729.975 907.21,465.155 907.886,324.043 908.563,447.003 909.239,468.861 909.916,540.034 910.592,420.086 911.269,572.447 911.945,750.592 \n",
       "  912.621,966.622 913.298,564.429 913.974,268.478 914.651,308.116 915.327,326.022 916.004,350.746 916.68,276.421 917.357,457.614 918.033,535.917 918.71,892.637 \n",
       "  919.386,521.749 920.062,225.09 920.739,531.743 921.415,491.785 922.092,308.974 922.768,221.551 923.445,371.191 924.121,282.041 924.798,356.62 925.474,583.458 \n",
       "  926.15,440.369 926.827,365.553 927.503,542.183 928.18,496.74 928.856,345.047 929.533,380.275 930.209,398.354 930.886,477.914 931.562,725.471 932.238,582.948 \n",
       "  932.915,448.802 933.591,351.026 934.268,400.647 934.944,425.94 935.621,395.097 936.297,471.578 936.974,429.865 937.65,535.403 938.326,300.984 939.003,428.989 \n",
       "  939.679,450.7 940.356,657.861 941.032,698.719 941.709,855.579 942.385,673.298 943.062,440.67 943.738,609.826 944.414,422.644 945.091,502.89 945.767,671.667 \n",
       "  946.444,413.96 947.12,440.193 947.797,438.167 948.473,876.343 949.15,691.454 949.826,759.535 950.503,959.933 951.179,361.096 951.855,370.112 952.532,302.719 \n",
       "  953.208,457.486 953.885,243.457 954.561,304.175 955.238,575.462 955.914,449.95 956.591,769.563 957.267,450.877 957.943,513.861 958.62,393.731 959.296,561.16 \n",
       "  959.973,524.164 960.649,364.162 961.326,408.794 962.002,412.952 962.679,679.832 963.355,450.193 964.031,307.667 964.708,398.756 965.384,385.922 966.061,399.035 \n",
       "  966.737,229.006 967.414,558.128 968.09,382.863 968.767,494.001 969.443,495.258 970.119,612.307 970.796,370.958 971.472,290.354 972.149,207.898 972.825,366.799 \n",
       "  973.502,521.703 974.178,327.335 974.855,268.978 975.531,468.382 976.207,256.381 976.884,465.299 977.56,507.429 978.237,484.422 978.913,535.204 979.59,672.977 \n",
       "  980.266,744.984 980.943,781.243 981.619,787.355 982.295,904.553 982.972,842.67 983.648,919.481 984.325,818.35 985.001,624.348 985.678,490.085 986.354,413.803 \n",
       "  987.031,520.013 987.707,511.383 988.384,696.394 989.06,495.21 989.736,699.657 990.413,521.541 991.089,658.424 991.766,616.032 992.442,370.088 993.119,387.559 \n",
       "  993.795,502.875 994.472,402.747 995.148,769.576 995.824,654.093 996.501,653.469 997.177,893.945 997.854,694.099 998.53,274.893 999.207,446.103 999.883,552.14 \n",
       "  1000.56,552.54 1001.24,604.697 1001.91,463.06 1002.59,448.739 1003.27,337.963 1003.94,420.118 1004.62,241.128 1005.29,449.723 1005.97,473.769 1006.65,481.317 \n",
       "  1007.32,370.077 1008,296.09 1008.68,426.388 1009.35,338.406 1010.03,342.342 1010.71,541.328 1011.38,616.15 1012.06,349.336 1012.74,543.984 1013.41,378.988 \n",
       "  1014.09,429.792 1014.76,544.646 1015.44,200.363 1016.12,308.729 1016.79,401.794 1017.47,557.131 1018.15,524.187 1018.82,592.607 1019.5,424.849 1020.18,647.556 \n",
       "  1020.85,595.338 1021.53,595.859 1022.21,242.494 1022.88,277.686 1023.56,649.386 1024.24,494.653 1024.91,401.944 1025.59,362.575 1026.26,813.815 1026.94,252.968 \n",
       "  1027.62,408.166 1028.29,317.126 1028.97,368.027 1029.65,390.766 1030.32,607.193 1031,756.059 1031.68,635.091 1032.35,531.955 1033.03,434.606 1033.71,547.692 \n",
       "  1034.38,666.903 1035.06,518.821 1035.73,867.075 1036.41,568.204 1037.09,702.209 1037.76,567.892 1038.44,419.268 1039.12,600.61 1039.79,400.791 1040.47,707.594 \n",
       "  1041.15,720.9 1041.82,412.408 1042.5,364.58 1043.18,364.975 1043.85,437.543 1044.53,537.35 1045.21,475.002 1045.88,441.732 1046.56,474.959 1047.23,366.787 \n",
       "  1047.91,289.583 1048.59,268.036 1049.26,433.423 1049.94,177.801 1050.62,333.877 1051.29,326.779 1051.97,630.191 1052.65,785.634 1053.32,243.293 1054,475.389 \n",
       "  1054.68,521.781 1055.35,152.162 1056.03,285.81 1056.7,253.28 1057.38,526.984 1058.06,444.539 1058.73,376.829 1059.41,582.165 1060.09,235.525 1060.76,457.324 \n",
       "  1061.44,532.551 1062.12,476.164 1062.79,424.563 1063.47,645.147 1064.15,514.325 1064.82,470.547 1065.5,406.826 1066.17,344.112 1066.85,240.366 1067.53,753.392 \n",
       "  1068.2,364.301 1068.88,512.635 1069.56,403.201 1070.23,354.668 1070.91,347.219 1071.59,339.147 1072.26,447.972 1072.94,411.145 1073.62,268.442 1074.29,328.628 \n",
       "  1074.97,474.497 1075.65,475.581 1076.32,438.692 1077,534.728 1077.67,742.05 1078.35,403.677 1079.03,485.074 1079.7,764.274 1080.38,793.555 1081.06,685.306 \n",
       "  1081.73,620.859 1082.41,329.134 1083.09,233.531 1083.76,459.576 1084.44,469.814 1085.12,251.73 1085.79,324.399 1086.47,278.809 1087.14,276.211 1087.82,346.102 \n",
       "  1088.5,304.453 1089.17,279.996 1089.85,273.811 1090.53,206.893 1091.2,324.314 1091.88,388.472 1092.56,334.958 1093.23,202.542 1093.91,412.772 1094.59,437.755 \n",
       "  1095.26,268.907 1095.94,391.682 1096.61,474.934 1097.29,706.45 1097.97,661.753 1098.64,698.183 1099.32,909.03 1100,885.68 1100.67,634.171 1101.35,644.323 \n",
       "  1102.03,668.407 1102.7,709.542 1103.38,814.896 1104.06,521.09 1104.73,654.602 1105.41,554.571 1106.09,695.915 1106.76,629.413 1107.44,767.778 1108.11,281.89 \n",
       "  1108.79,343.106 1109.47,579.248 1110.14,186.361 1110.82,442.547 1111.5,597.835 1112.17,467.585 1112.85,780.389 1113.53,484.723 1114.2,664.597 1114.88,512.274 \n",
       "  1115.56,192.858 1116.23,311.066 1116.91,287.126 1117.58,432.986 1118.26,472.856 1118.94,461.8 1119.61,491.161 1120.29,437.664 1120.97,340.768 1121.64,156.656 \n",
       "  1122.32,405.008 1123,361.475 1123.67,373.189 1124.35,377.819 1125.03,489.465 1125.7,553.614 1126.38,423.976 1127.06,488.97 1127.73,403.391 1128.41,482.136 \n",
       "  1129.08,564.102 1129.76,362.902 1130.44,272.025 1131.11,614.982 1131.79,668.694 1132.47,445.517 1133.14,686.603 1133.82,560.723 1134.5,238.135 1135.17,301.232 \n",
       "  1135.85,492.785 1136.53,498.602 1137.2,470.621 1137.88,372.732 1138.55,659.597 1139.23,570.843 1139.91,712.77 1140.58,736.368 1141.26,394.702 1141.94,461.484 \n",
       "  1142.61,561.724 1143.29,399.399 1143.97,324.527 1144.64,396.854 1145.32,233.898 1146,368.293 1146.67,517.257 1147.35,519.689 1148.02,368.166 1148.7,447.264 \n",
       "  1149.38,723.852 1150.05,593.177 1150.73,183.265 1151.41,418.47 1152.08,533.395 1152.76,355.928 1153.44,446.653 1154.11,326.695 1154.79,274.34 1155.47,322.211 \n",
       "  1156.14,372.773 1156.82,734.631 1157.5,468.053 1158.17,458.581 1158.85,387.451 1159.52,187.461 1160.2,479.21 1160.88,658.995 1161.55,475.27 1162.23,335.052 \n",
       "  1162.91,498.598 1163.58,471.074 1164.26,410.79 1164.94,306.094 1165.61,484.369 1166.29,323.008 1166.97,355.089 1167.64,308.063 1168.32,409.589 1168.99,326.496 \n",
       "  1169.67,539.132 1170.35,668.935 1171.02,347.244 1171.7,576.697 1172.38,537.925 1173.05,491.236 1173.73,447.945 1174.41,494.368 1175.08,620.003 1175.76,711.869 \n",
       "  1176.44,440.179 1177.11,633.463 1177.79,686.517 1178.46,670.406 1179.14,616.978 1179.82,684.554 1180.49,727.991 1181.17,608.233 1181.85,561.721 1182.52,294.429 \n",
       "  1183.2,540.019 1183.88,405.797 1184.55,343.007 1185.23,317.316 1185.91,328.132 1186.58,327.315 1187.26,321.31 1187.94,524.086 1188.61,572.692 1189.29,449.495 \n",
       "  1189.96,630.029 1190.64,455.311 1191.32,313.599 1191.99,838.003 1192.67,429.206 1193.35,718.043 1194.02,523.909 1194.7,344.736 1195.38,233.823 1196.05,252.949 \n",
       "  1196.73,214.28 1197.41,521.965 1198.08,259.472 1198.76,243.071 1199.43,471.316 1200.11,396.546 1200.79,372.661 1201.46,488.931 1202.14,477.798 1202.82,366.161 \n",
       "  1203.49,396.198 1204.17,576.502 1204.85,359.575 1205.52,614.545 1206.2,566.422 1206.88,496.629 1207.55,424.873 1208.23,270.418 1208.91,515.376 1209.58,647.171 \n",
       "  1210.26,409.499 1210.93,209.68 1211.61,567.513 1212.29,650.798 1212.96,319.999 1213.64,482.126 1214.32,233.783 1214.99,356.341 1215.67,436.747 1216.35,387.061 \n",
       "  1217.02,405.968 1217.7,381.64 1218.38,462.406 1219.05,505.033 1219.73,597.078 1220.4,742.124 1221.08,619.996 1221.76,635.414 1222.43,724.799 1223.11,526.296 \n",
       "  1223.79,757.013 1224.46,356.441 1225.14,334.827 1225.82,295.578 1226.49,341.636 1227.17,494.855 1227.85,757.042 1228.52,639.057 1229.2,520.085 1229.87,740.886 \n",
       "  1230.55,664.384 1231.23,634.198 1231.9,1005.02 1232.58,623.616 1233.26,369.653 1233.93,155.242 1234.61,241.059 1235.29,444.357 1235.96,469.349 1236.64,284.636 \n",
       "  1237.32,217.57 1237.99,268.746 1238.67,458.118 1239.35,785.812 1240.02,464.971 1240.7,251.888 1241.37,403.063 1242.05,500.588 1242.73,683.03 1243.4,419.998 \n",
       "  1244.08,515.295 1244.76,300.272 1245.43,422.419 1246.11,510.196 1246.79,451.764 1247.46,419.723 1248.14,608.857 1248.82,555.165 1249.49,280.747 1250.17,368.629 \n",
       "  1250.84,560.479 1251.52,586.804 1252.2,574.878 1252.87,526.128 1253.55,342.686 1254.23,295.207 1254.9,320.482 1255.58,341.919 1256.26,454.174 1256.93,270.001 \n",
       "  1257.61,552.692 1258.29,472.34 1258.96,530.278 1259.64,462.566 1260.32,510.147 1260.99,306.792 1261.67,417.416 1262.34,316.645 1263.02,412.211 1263.7,479.72 \n",
       "  1264.37,185.201 1265.05,292.502 1265.73,457.004 1266.4,428.281 1267.08,477.853 1267.76,325.368 1268.43,382.39 1269.11,319.849 1269.79,514.818 1270.46,366.562 \n",
       "  1271.14,715.441 1271.81,531.199 1272.49,239.092 1273.17,208.903 1273.84,393.862 1274.52,307.562 1275.2,204.487 1275.87,264.431 1276.55,316.725 1277.23,216.091 \n",
       "  1277.9,420.914 1278.58,401.113 1279.26,211.01 1279.93,453.79 1280.61,447.724 1281.28,1072.23 1281.96,690.617 1282.64,668.091 1283.31,491.222 1283.99,784.975 \n",
       "  1284.67,584.34 1285.34,728.592 1286.02,545.477 1286.7,600.279 1287.37,904.744 1288.05,639.279 1288.73,741.568 1289.4,761.733 1290.08,930.899 1290.76,645.31 \n",
       "  1291.43,690.824 1292.11,594.749 1292.78,304.523 1293.46,370.242 1294.14,292.68 1294.81,459.619 1295.49,354.328 1296.17,390.409 1296.84,503.195 1297.52,484.41 \n",
       "  1298.2,370.822 1298.87,514.95 1299.55,443.393 1300.23,696.973 1300.9,598.907 1301.58,715.41 1302.25,877.628 1302.93,719.993 1303.61,325.885 1304.28,492.068 \n",
       "  1304.96,346.394 1305.64,450.769 1306.31,341.865 1306.99,279.154 1307.67,234.368 1308.34,313.609 1309.02,221.509 1309.7,402.544 1310.37,415.149 1311.05,493.603 \n",
       "  1311.72,390.225 1312.4,473.344 1313.08,622.228 1313.75,611.796 1314.43,480.233 1315.11,316.739 1315.78,404.555 1316.46,381.863 1317.14,405.649 1317.81,556.703 \n",
       "  1318.49,573.173 1319.17,403.718 1319.84,282.262 1320.52,765.42 1321.2,539.391 1321.87,347.455 1322.55,343.403 1323.22,355.15 1323.9,604.848 1324.58,740.085 \n",
       "  1325.25,756.37 1325.93,560.889 1326.61,308.402 1327.28,320.661 1327.96,157.102 1328.64,195.021 1329.31,271.233 1329.99,271.793 1330.67,373.459 1331.34,236.623 \n",
       "  1332.02,432.365 1332.69,400.149 1333.37,405.498 1334.05,444.593 1334.72,419.505 1335.4,366.65 1336.08,609.191 1336.75,227.795 1337.43,497.387 1338.11,581.377 \n",
       "  1338.78,490.798 1339.46,607.386 1340.14,423.095 1340.81,397.135 1341.49,228.487 1342.17,430.999 1342.84,573.815 1343.52,417.496 1344.19,388.226 1344.87,386.776 \n",
       "  1345.55,631.2 1346.22,524.649 1346.9,364.781 1347.58,236.684 1348.25,310.082 1348.93,476.511 1349.61,628.753 1350.28,629.091 1350.96,778.67 1351.64,819.424 \n",
       "  1352.31,480.671 1352.99,725.075 1353.66,259.023 1354.34,218.518 1355.02,341.514 1355.69,288.244 1356.37,220.023 1357.05,275.854 1357.72,504.482 1358.4,346.377 \n",
       "  1359.08,479.359 1359.75,740.846 1360.43,1046.2 1361.11,530.465 1361.78,650.705 1362.46,569.424 1363.13,491.78 1363.81,301.482 1364.49,320.486 1365.16,647.607 \n",
       "  1365.84,541.48 1366.52,472.449 1367.19,672.038 1367.87,479.553 1368.55,637.077 1369.22,764.98 1369.9,887.536 1370.58,490.455 1371.25,440.461 1371.93,600.452 \n",
       "  1372.61,593.135 1373.28,591.337 1373.96,378.685 1374.63,441.524 1375.31,729.995 1375.99,286.979 1376.66,615.243 1377.34,458.161 1378.02,540.587 1378.69,481.072 \n",
       "  1379.37,591.579 1380.05,587.154 1380.72,701.641 1381.4,708.51 1382.08,625.051 1382.75,676.253 1383.43,763.686 1384.1,677.599 1384.78,546.385 1385.46,272.707 \n",
       "  1386.13,503.085 1386.81,527.266 1387.49,546.698 1388.16,552.232 1388.84,612.382 1389.52,393.577 1390.19,487.829 1390.87,667.058 1391.55,669.798 1392.22,712.109 \n",
       "  1392.9,588.696 1393.57,760.215 1394.25,758.575 1394.93,239.32 1395.6,251.45 1396.28,444.995 1396.96,332.532 1397.63,632.824 1398.31,441.749 1398.99,482.644 \n",
       "  1399.66,437.625 1400.34,420.073 1401.02,268.813 1401.69,439.906 1402.37,374.356 1403.05,452.154 1403.72,493.819 1404.4,509.748 1405.07,338.5 1405.75,350.925 \n",
       "  1406.43,307.66 1407.1,423.515 1407.78,539.831 1408.46,391.026 1409.13,273.865 1409.81,602.196 1410.49,561.529 1411.16,375.094 1411.84,719.429 1412.52,321.93 \n",
       "  1413.19,598.912 1413.87,484.481 1414.54,418.444 1415.22,275.43 1415.9,298.22 1416.57,318.495 1417.25,463.078 1417.93,582.687 1418.6,758.701 1419.28,672.117 \n",
       "  1419.96,622.683 1420.63,605.234 1421.31,542.879 1421.99,715.818 1422.66,353.1 1423.34,356.363 1424.02,293.138 1424.69,510.665 1425.37,296.526 1426.04,231.43 \n",
       "  1426.72,388.028 1427.4,439.804 1428.07,275.941 1428.75,353.481 1429.43,412.759 1430.1,600.643 1430.78,369.585 1431.46,515.173 1432.13,531.776 1432.81,499.625 \n",
       "  1433.49,502.99 1434.16,541.032 1434.84,401.701 1435.51,224.786 1436.19,213.178 1436.87,278.513 1437.54,721.212 1438.22,373.473 1438.9,516.256 1439.57,447.985 \n",
       "  1440.25,273.463 1440.93,490.303 1441.6,397.722 1442.28,494.941 1442.96,682.9 1443.63,559.286 1444.31,505.647 1444.98,791.127 1445.66,450.635 1446.34,238.092 \n",
       "  1447.01,381.873 1447.69,342.948 1448.37,580.279 1449.04,303.205 1449.72,506.483 1450.4,445.138 1451.07,543.224 1451.75,517.069 1452.43,213.357 1453.1,287.484 \n",
       "  1453.78,255.962 1454.46,164.008 1455.13,462.376 1455.81,530.988 1456.48,651.524 1457.16,541.798 1457.84,528.869 1458.51,492.472 1459.19,357.669 1459.87,409.944 \n",
       "  1460.54,249.568 1461.22,493.179 1461.9,333.796 1462.57,343.194 1463.25,579.174 1463.93,495.443 1464.6,365.334 1465.28,574.014 1465.95,582.78 1466.63,485.725 \n",
       "  1467.31,757.284 1467.98,673.84 1468.66,872.389 1469.34,775.613 1470.01,991.135 1470.69,170.183 1471.37,347.369 1472.04,446.129 1472.72,663.659 1473.4,663.219 \n",
       "  1474.07,344.317 1474.75,538.275 1475.43,571.903 1476.1,313.639 1476.78,309.068 1477.45,437.035 1478.13,303.388 1478.81,455.261 1479.48,409.41 1480.16,356.345 \n",
       "  1480.84,518.081 1481.51,369.774 1482.19,842.556 1482.87,546.818 1483.54,603.445 1484.22,499.226 1484.9,328.62 1485.57,372.412 1486.25,384.08 1486.92,239.027 \n",
       "  1487.6,548.485 1488.28,622.498 1488.95,538.678 1489.63,293.819 1490.31,713.363 1490.98,508.251 1491.66,256.351 1492.34,498.776 1493.01,354.426 1493.69,342.408 \n",
       "  1494.37,349.998 1495.04,407.413 1495.72,681.596 1496.39,378.574 1497.07,181.774 1497.75,441.163 1498.42,246.256 1499.1,869.591 1499.78,604.162 1500.45,192.913 \n",
       "  1501.13,570.404 1501.81,349.155 1502.48,297.429 1503.16,220.657 1503.84,262.2 1504.51,260.896 1505.19,352.877 1505.87,543.733 1506.54,369.787 1507.22,276.405 \n",
       "  1507.89,367.19 1508.57,390.505 1509.25,561.793 1509.92,431.209 1510.6,601.306 1511.28,565.644 1511.95,740.65 1512.63,407.497 1513.31,499.829 1513.98,244.74 \n",
       "  1514.66,267.091 1515.34,595.245 1516.01,240.699 1516.69,312.719 1517.36,360.997 1518.04,729.125 1518.72,314.769 1519.39,565.146 1520.07,639.549 1520.75,605.821 \n",
       "  1521.42,473.705 1522.1,468.909 1522.78,762.576 1523.45,638.915 1524.13,314.459 1524.81,375.058 1525.48,226.796 1526.16,441.66 1526.83,422.557 1527.51,443.238 \n",
       "  1528.19,315.102 1528.86,204.591 1529.54,352.408 1530.22,622.858 1530.89,237.581 1531.57,339.836 1532.25,200.677 1532.92,535.651 1533.6,511.734 1534.28,449.208 \n",
       "  1534.95,489.177 1535.63,442.44 1536.31,512.257 1536.98,544.147 1537.66,635.705 1538.33,451.877 1539.01,302.393 1539.69,511.385 1540.36,314.237 1541.04,303.588 \n",
       "  1541.72,453.829 1542.39,842.803 1543.07,613.47 1543.75,610.505 1544.42,233.185 1545.1,699.887 1545.78,417.392 1546.45,227.844 1547.13,441.094 1547.8,383.665 \n",
       "  1548.48,379.36 1549.16,264.861 1549.83,387.758 1550.51,349.311 1551.19,360.111 1551.86,397.432 1552.54,410.496 1553.22,428.886 1553.89,445.292 1554.57,531.822 \n",
       "  1555.25,224.968 1555.92,453.063 1556.6,878.354 1557.28,546.534 1557.95,439.284 1558.63,560.555 1559.3,417.574 1559.98,480.318 1560.66,547.369 1561.33,650.849 \n",
       "  1562.01,669.639 1562.69,277.573 1563.36,244.882 1564.04,329.188 1564.72,278.183 1565.39,222.242 1566.07,433.948 1566.75,319.782 1567.42,315.053 1568.1,408.946 \n",
       "  1568.77,429.545 1569.45,489.797 1570.13,618.676 1570.8,598.774 1571.48,680.902 1572.16,365.524 1572.83,347.388 1573.51,193.303 1574.19,418.679 1574.86,387.811 \n",
       "  1575.54,579.738 1576.22,471.377 1576.89,520.242 1577.57,479.239 1578.24,366.708 1578.92,355.893 1579.6,335.614 1580.27,355.288 1580.95,418.938 1581.63,355.448 \n",
       "  1582.3,314.843 1582.98,527.964 1583.66,259.452 1584.33,473.262 1585.01,380.506 1585.69,513.075 1586.36,535.204 1587.04,351.611 1587.72,345.867 1588.39,426.299 \n",
       "  1589.07,486.687 1589.74,197.106 1590.42,657.973 1591.1,566.923 1591.77,520.392 1592.45,495.565 1593.13,168.567 1593.8,344.075 1594.48,313.229 1595.16,574.222 \n",
       "  1595.83,658.512 1596.51,357.912 1597.19,476.667 1597.86,324.806 1598.54,402.454 1599.21,632.414 1599.89,751.62 1600.57,373.536 1601.24,404.002 1601.92,399.607 \n",
       "  1602.6,389.757 1603.27,315.972 1603.95,334.515 1604.63,448.121 1605.3,426.717 1605.98,588.978 1606.66,376.21 1607.33,877.341 1608.01,660.112 1608.68,377.017 \n",
       "  1609.36,338.599 1610.04,618.575 1610.71,539.509 1611.39,671.568 1612.07,499.028 1612.74,462.444 1613.42,637.327 1614.1,506.261 1614.77,483.799 1615.45,433.992 \n",
       "  1616.13,427.349 1616.8,388.225 1617.48,533.259 1618.16,542.501 1618.83,441.067 1619.51,431.987 1620.18,160.581 1620.86,233.616 1621.54,321.887 1622.21,246.179 \n",
       "  1622.89,719.081 1623.57,526.568 1624.24,418.517 1624.92,725.726 1625.6,587.512 1626.27,564.216 1626.95,491.621 1627.63,411.326 1628.3,491.79 1628.98,308.398 \n",
       "  1629.65,281.3 1630.33,457.513 1631.01,182.449 1631.68,388.028 1632.36,310.962 1633.04,293.049 1633.71,367.859 1634.39,329.953 1635.07,437.802 1635.74,468.057 \n",
       "  1636.42,306.014 1637.1,370.34 1637.77,336.742 1638.45,290.474 1639.13,225.438 1639.8,497.224 1640.48,422.836 1641.15,466.676 1641.83,414.3 1642.51,451.219 \n",
       "  1643.18,590.358 1643.86,988.819 1644.54,862.279 1645.21,649.121 1645.89,929.103 1646.57,568.148 1647.24,865.383 1647.92,527.458 1648.6,314.94 1649.27,348.899 \n",
       "  1649.95,444.87 1650.62,292.93 1651.3,363.613 1651.98,216.014 1652.65,318.905 1653.33,427.559 1654.01,311.559 1654.68,458.464 1655.36,562.387 1656.04,612.288 \n",
       "  1656.71,409.71 1657.39,565.705 1658.07,386.929 1658.74,573.682 1659.42,332.327 1660.09,441.542 1660.77,538.469 1661.45,378.39 1662.12,412.934 1662.8,254.966 \n",
       "  1663.48,458.237 1664.15,233.988 1664.83,343.784 1665.51,257.766 1666.18,366.917 1666.86,315.072 1667.54,366.454 1668.21,432.411 1668.89,255.701 1669.57,334.516 \n",
       "  1670.24,185.799 1670.92,207.375 1671.59,433.613 1672.27,509.887 1672.95,472.272 1673.62,334.308 1674.3,426.492 1674.98,605.561 1675.65,537.747 1676.33,459.878 \n",
       "  1677.01,740.662 1677.68,748.794 1678.36,569.304 1679.04,737.131 1679.71,319.52 1680.39,531.875 1681.06,280.07 1681.74,196.424 1682.42,272.983 1683.09,447.106 \n",
       "  1683.77,385.336 1684.45,440.145 1685.12,343.135 1685.8,370.492 1686.48,646.649 1687.15,460.47 1687.83,568.299 1688.51,577.933 1689.18,582.123 1689.86,472.803 \n",
       "  1690.54,294.458 1691.21,308.316 1691.89,344.153 1692.56,375.529 1693.24,482.773 1693.92,227.998 1694.59,554.596 1695.27,410.485 1695.95,517.607 1696.62,409.357 \n",
       "  1697.3,355.373 1697.98,247.636 1698.65,273.754 1699.33,299.362 1700.01,519.926 1700.68,413.343 1701.36,583.529 1702.03,362.214 1702.71,353.498 1703.39,359.619 \n",
       "  1704.06,903.564 1704.74,543.846 1705.42,751.191 1706.09,311.597 1706.77,161.889 1707.45,231.275 1708.12,297.12 1708.8,400.022 1709.48,250.668 1710.15,250.206 \n",
       "  1710.83,428.567 1711.5,536.157 1712.18,430.359 1712.86,288.103 1713.53,504.048 1714.21,393.855 1714.89,368.544 1715.56,369.41 1716.24,444.712 1716.92,562.333 \n",
       "  1717.59,459.328 1718.27,553.416 1718.95,320.989 1719.62,647.36 1720.3,497.001 1720.98,535.594 1721.65,525.087 1722.33,715.193 1723,960.497 1723.68,1143 \n",
       "  1724.36,1008.32 1725.03,1067.58 1725.71,430.833 1726.39,690.595 1727.06,425.683 1727.74,701.12 1728.42,655.278 1729.09,758.355 1729.77,774.667 1730.45,871.775 \n",
       "  1731.12,838.931 1731.8,1193.28 1732.47,606.453 1733.15,700.645 1733.83,279.307 1734.5,406.244 1735.18,375.644 1735.86,358.809 1736.53,130.047 1737.21,329.035 \n",
       "  1737.89,243.232 1738.56,405.269 1739.24,244.224 1739.92,298.436 1740.59,332.687 1741.27,414.468 1741.94,482.915 1742.62,742.827 1743.3,465.194 1743.97,570.386 \n",
       "  1744.65,393.21 1745.33,641.918 1746,481.169 1746.68,360.481 1747.36,455.538 1748.03,320.311 1748.71,373.896 1749.39,621.95 1750.06,397.341 1750.74,405.527 \n",
       "  1751.42,489.716 1752.09,617.956 1752.77,463.982 1753.44,588.228 1754.12,491.459 1754.8,475.135 1755.47,452.044 1756.15,331.514 1756.83,376.935 1757.5,639.257 \n",
       "  1758.18,410.877 1758.86,426.587 1759.53,353.455 1760.21,430.619 1760.89,233.093 1761.56,504.367 1762.24,404.677 1762.91,504.366 1763.59,322.77 1764.27,349.058 \n",
       "  1764.94,649.516 1765.62,366.29 1766.3,335.485 1766.97,216.493 1767.65,274.216 1768.33,616.24 1769,504.453 1769.68,572.179 1770.36,377.357 1771.03,532.467 \n",
       "  1771.71,657.927 1772.39,575.794 1773.06,366.802 1773.74,755.825 1774.41,595.75 1775.09,426.878 1775.77,336.427 1776.44,558.267 1777.12,603.514 1777.8,367.857 \n",
       "  1778.47,465.932 1779.15,617.429 1779.83,383.785 1780.5,475.613 1781.18,345.733 1781.86,385.526 1782.53,332.001 1783.21,316.946 1783.88,337.771 1784.56,460.985 \n",
       "  1785.24,413.643 1785.91,436.579 1786.59,529.012 1787.27,596.985 1787.94,273.608 1788.62,622.197 1789.3,415.087 1789.97,272.639 1790.65,463.338 1791.33,245.501 \n",
       "  1792,429.68 1792.68,226.427 1793.35,686.453 1794.03,428.727 1794.71,621.963 1795.38,380.624 1796.06,351.69 1796.74,484.244 1797.41,120.11 1798.09,236.685 \n",
       "  1798.77,591.102 1799.44,453.405 1800.12,525.611 1800.8,439.86 1801.47,351.154 1802.15,563.75 1802.83,416.923 1803.5,504.593 1804.18,308.963 1804.85,398.517 \n",
       "  1805.53,787.153 1806.21,595.447 1806.88,535.795 1807.56,579.092 1808.24,355.946 1808.91,464.903 1809.59,409.233 1810.27,526.263 1810.94,515.097 1811.62,620.163 \n",
       "  1812.3,538.595 1812.97,600.802 1813.65,524.934 1814.32,844.596 1815,1029.1 1815.68,337.276 1816.35,490.484 1817.03,493.993 1817.71,418.725 1818.38,540.168 \n",
       "  1819.06,329.953 1819.74,323.324 1820.41,408.965 1821.09,663.375 1821.77,428.152 1822.44,747.947 1823.12,285.098 1823.79,454.06 1824.47,423.977 1825.15,342.871 \n",
       "  1825.82,372.883 1826.5,446.794 1827.18,348.621 1827.85,401.448 1828.53,585.151 1829.21,214.996 1829.88,340.161 1830.56,321.93 1831.24,342.698 1831.91,890.597 \n",
       "  1832.59,531.714 1833.27,543.572 1833.94,463.287 1834.62,638.176 1835.29,426.916 1835.97,708.113 1836.65,498.403 1837.32,502.133 1838,608.096 1838.68,661.426 \n",
       "  1839.35,560.44 1840.03,420.441 1840.71,431.607 1841.38,647.311 1842.06,346.48 1842.74,334.122 1843.41,385.233 1844.09,225.654 1844.76,392.105 1845.44,266.416 \n",
       "  1846.12,550.536 1846.79,367.747 1847.47,241.466 1848.15,415.18 1848.82,558.163 1849.5,375.284 1850.18,371.588 1850.85,209.178 1851.53,616.258 1852.21,627.813 \n",
       "  1852.88,784.095 1853.56,786.767 1854.24,705.821 1854.91,686.066 1855.59,654.446 1856.26,710.958 1856.94,928.264 1857.62,496.532 1858.29,245.318 1858.97,322.419 \n",
       "  1859.65,418.935 1860.32,640.294 1861,565.04 1861.68,584.831 1862.35,347.195 1863.03,304.781 1863.71,498.897 1864.38,512.371 1865.06,389.449 1865.73,652.91 \n",
       "  1866.41,1386.61 1867.09,1119.71 1867.76,225.156 1868.44,304.482 1869.12,171.426 1869.79,214.178 1870.47,304.072 1871.15,356.443 1871.82,516.366 1872.5,192.938 \n",
       "  1873.18,261.915 1873.85,521.251 1874.53,290.261 1875.2,617.8 1875.88,392.139 1876.56,400.83 1877.23,464.144 1877.91,438.623 1878.59,558.443 1879.26,470.763 \n",
       "  1879.94,304.92 1880.62,268.973 1881.29,492.979 1881.97,682.003 1882.65,605.845 1883.32,497.712 1884,669.916 1884.68,508.843 1885.35,669.128 1886.03,640.046 \n",
       "  1886.7,395.013 1887.38,470.394 1888.06,354.536 1888.73,358.974 1889.41,393.35 1890.09,223.758 1890.76,479.896 1891.44,492.275 1892.12,330.794 1892.79,554.66 \n",
       "  1893.47,488.28 1894.15,642.936 1894.82,439.891 1895.5,152.577 1896.17,398.75 1896.85,345.205 1897.53,548.833 1898.2,719.642 1898.88,560.761 1899.56,654.007 \n",
       "  1900.23,322.987 1900.91,296.866 1901.59,294.739 1902.26,340.382 1902.94,989.781 1903.62,693.086 1904.29,426.357 1904.97,300.079 1905.65,269.669 1906.32,444.903 \n",
       "  1907,401.476 1907.67,170.296 1908.35,364.43 1909.03,309.966 1909.7,385.042 1910.38,364.648 1911.06,334.674 1911.73,400.012 1912.41,303.678 1913.09,403.689 \n",
       "  1913.76,339.606 1914.44,416.043 1915.12,549.145 1915.79,526.397 1916.47,469.042 1917.14,86.2547 1917.82,253.553 1918.5,294.509 1919.17,213.228 1919.85,395.307 \n",
       "  1920.53,535.1 1921.2,647.717 1921.88,755.479 1922.56,403.019 1923.23,489.292 1923.91,612.794 1924.59,516.795 1925.26,247.325 1925.94,341.78 1926.61,362.431 \n",
       "  1927.29,732.793 1927.97,493.779 1928.64,694.258 1929.32,570.997 1930,508.785 1930.67,671.719 1931.35,605.65 1932.03,328.289 1932.7,359.095 1933.38,384.171 \n",
       "  1934.06,262.784 1934.73,184.743 1935.41,278.262 1936.09,488.09 1936.76,378.062 1937.44,464.367 1938.11,541.813 1938.79,616.95 1939.47,477.706 1940.14,344.26 \n",
       "  1940.82,386.374 1941.5,389.195 1942.17,438.834 1942.85,589.824 1943.53,489.681 1944.2,679.942 1944.88,549.299 1945.56,497.391 1946.23,920.669 1946.91,886.129 \n",
       "  1947.58,1007.71 1948.26,863.176 1948.94,663.41 1949.61,872.622 1950.29,401.42 1950.97,418.392 1951.64,334.324 1952.32,303.408 1953,269.413 1953.67,344.315 \n",
       "  1954.35,780.861 1955.03,584.796 1955.7,584.38 1956.38,298.994 1957.05,724.854 1957.73,522.704 1958.41,633.864 1959.08,625.013 1959.76,687.294 1960.44,230.463 \n",
       "  1961.11,196.439 1961.79,370.638 1962.47,377.831 1963.14,252.364 1963.82,557.247 1964.5,461.393 1965.17,292.708 1965.85,508.917 1966.53,353.527 1967.2,343.804 \n",
       "  1967.88,483.256 1968.55,585.505 1969.23,520.803 1969.91,670.311 1970.58,224.376 1971.26,229.969 1971.94,202.551 1972.61,397.339 1973.29,540.864 1973.97,404.234 \n",
       "  1974.64,585.875 1975.32,397.983 1976,537.932 1976.67,327.28 1977.35,537.132 1978.02,429.731 1978.7,410.199 1979.38,486.758 1980.05,623.284 1980.73,373.876 \n",
       "  1981.41,219.805 1982.08,572.039 1982.76,581.73 1983.44,595.72 1984.11,493.91 1984.79,751.087 1985.47,763.157 1986.14,653.271 1986.82,869.244 1987.5,448.7 \n",
       "  1988.17,483.039 1988.85,891.834 1989.52,744.542 1990.2,457.189 1990.88,466.426 1991.55,696.553 1992.23,330.184 1992.91,501.012 1993.58,240.073 1994.26,481.357 \n",
       "  1994.94,476.774 1995.61,437.718 1996.29,512.439 1996.97,615.074 1997.64,289.334 1998.32,461.791 1998.99,258.781 1999.67,242.547 2000.35,517.267 2001.02,535.92 \n",
       "  2001.7,432.05 2002.38,498.45 2003.05,276.397 2003.73,350.452 2004.41,613.495 2005.08,304.396 2005.76,513.802 2006.44,415.868 2007.11,229.274 2007.79,416.58 \n",
       "  2008.46,358.817 2009.14,476.019 2009.82,557.985 2010.49,698.439 2011.17,707.026 2011.85,760.412 2012.52,404.209 2013.2,545.542 2013.88,425.522 2014.55,632.792 \n",
       "  2015.23,132.254 2015.91,302.364 2016.58,485.391 2017.26,372.189 2017.94,514.413 2018.61,595.345 2019.29,616.996 2019.96,459.961 2020.64,505.869 2021.32,543.425 \n",
       "  2021.99,558.211 2022.67,364.192 2023.35,397.015 2024.02,452.758 2024.7,465.89 2025.38,685.104 2026.05,498.191 2026.73,515.328 2027.41,312.149 2028.08,258.946 \n",
       "  2028.76,353.691 2029.43,476.771 2030.11,167.738 2030.79,440.19 2031.46,312.566 2032.14,440.942 2032.82,500.914 2033.49,683.953 2034.17,745.062 2034.85,620.32 \n",
       "  2035.52,540.734 2036.2,642.587 2036.88,648.205 2037.55,616.628 2038.23,396.727 2038.91,334.583 2039.58,214.511 2040.26,604.623 2040.93,519.874 2041.61,947.074 \n",
       "  2042.29,602.981 2042.96,452.292 2043.64,356.567 2044.32,399.956 2044.99,400.659 2045.67,281.144 2046.35,476.441 2047.02,412.132 2047.7,374.966 2048.38,310.824 \n",
       "  2049.05,285.579 2049.73,360.953 2050.4,401.18 2051.08,480.457 2051.76,311.106 2052.43,500.264 2053.11,461.633 2053.79,555.284 2054.46,329.036 2055.14,323.819 \n",
       "  2055.82,274.027 2056.49,307.44 2057.17,381.654 2057.85,597.796 2058.52,531.949 2059.2,444.76 2059.87,552.146 2060.55,377.411 2061.23,526.279 2061.9,414.548 \n",
       "  2062.58,334.05 2063.26,544.69 2063.93,279.805 2064.61,442.569 2065.29,451.507 2065.96,376.004 2066.64,356.434 2067.32,536.523 2067.99,455.109 2068.67,681.533 \n",
       "  2069.35,595.917 2070.02,835.126 2070.7,435.454 2071.37,408.059 2072.05,477.473 2072.73,582.822 2073.4,493.119 2074.08,589.553 2074.76,814.088 2075.43,741.614 \n",
       "  2076.11,811.021 2076.79,970.051 2077.46,1062.07 2078.14,924.909 2078.82,982.799 2079.49,540.412 2080.17,481.625 2080.84,449.926 2081.52,360.245 2082.2,533.103 \n",
       "  2082.87,465.991 2083.55,426.029 2084.23,232.87 2084.9,294.226 2085.58,302.874 2086.26,491.111 2086.93,371.284 2087.61,370.238 2088.29,417.782 2088.96,458.566 \n",
       "  2089.64,438.445 2090.31,547.599 2090.99,404.83 2091.67,714.448 2092.34,677.721 2093.02,815.222 2093.7,904.397 2094.37,963.848 2095.05,616.609 2095.73,674.032 \n",
       "  2096.4,827.611 2097.08,716.783 2097.76,758.668 2098.43,743.65 2099.11,725.136 2099.79,774.856 2100.46,638.028 2101.14,239.297 2101.81,290.866 2102.49,336.951 \n",
       "  2103.17,193.389 2103.84,396.346 2104.52,491.603 2105.2,533.322 2105.87,607.612 2106.55,642.072 2107.23,813.824 2107.9,655.512 2108.58,810.931 2109.26,910.304 \n",
       "  2109.93,487.863 2110.61,527.391 2111.28,457.079 2111.96,529.682 2112.64,476.556 2113.31,474.408 2113.99,716.248 2114.67,656.429 2115.34,441.519 2116.02,237.717 \n",
       "  2116.7,292.17 2117.37,346.437 2118.05,454.87 2118.73,376.065 2119.4,363.984 2120.08,488.467 2120.76,539.057 2121.43,360.411 2122.11,205.871 2122.78,190.537 \n",
       "  2123.46,584.99 2124.14,393.632 2124.81,411.629 2125.49,629.124 2126.17,542.104 2126.84,725.543 2127.52,738.483 2128.2,303.754 2128.87,511.959 2129.55,217.172 \n",
       "  2130.23,355.949 2130.9,580.3 2131.58,452.157 2132.25,247.216 2132.93,400.835 2133.61,436.035 2134.28,531.004 2134.96,550.836 2135.64,484.599 2136.31,679.47 \n",
       "  2136.99,564.261 2137.67,545.179 2138.34,299.831 2139.02,139.597 2139.7,358.887 2140.37,334.037 2141.05,645.082 2141.72,408.249 2142.4,347.279 2143.08,382.4 \n",
       "  2143.75,542.782 2144.43,396.733 2145.11,355.894 2145.78,612.715 2146.46,510.273 2147.14,330.849 2147.81,371.092 2148.49,98.4542 2149.17,158.059 2149.84,250.79 \n",
       "  2150.52,619.651 2151.2,216.315 2151.87,379.051 2152.55,480.542 2153.22,522.541 2153.9,424.416 2154.58,206.367 2155.25,357.781 2155.93,352.552 2156.61,355.751 \n",
       "  2157.28,372.215 2157.96,406.324 2158.64,403.99 2159.31,726.803 2159.99,572.76 2160.67,525.046 2161.34,288.244 2162.02,275.208 2162.69,355.412 2163.37,398.38 \n",
       "  2164.05,374.117 2164.72,493.304 2165.4,214.083 2166.08,515.096 2166.75,226.597 2167.43,402.805 2168.11,459.744 2168.78,383.694 2169.46,587.903 2170.14,547.269 \n",
       "  2170.81,760.487 2171.49,359.797 2172.16,599.447 2172.84,404.59 2173.52,339.567 2174.19,219.105 2174.87,457.183 2175.55,366.159 2176.22,320 2176.9,338.551 \n",
       "  2177.58,349.169 2178.25,434.377 2178.93,310.28 2179.61,450.501 2180.28,657.964 2180.96,537.163 2181.64,430.108 2182.31,443.963 2182.99,440.136 2183.66,599.845 \n",
       "  2184.34,294.797 2185.02,387.713 2185.69,413.781 2186.37,458.071 2187.05,426.259 2187.72,624.059 2188.4,377.98 2189.08,276.773 2189.75,327.093 2190.43,280.016 \n",
       "  2191.11,291.596 2191.78,239.859 2192.46,190.322 2193.13,256.726 2193.81,512.44 2194.49,366.103 2195.16,349.808 2195.84,406.04 2196.52,524.455 2197.19,281.03 \n",
       "  2197.87,446.601 2198.55,262.529 2199.22,194.639 2199.9,333.587 2200.58,506.243 2201.25,486.582 2201.93,634.487 2202.61,492.474 2203.28,602.807 2203.96,704.821 \n",
       "  2204.63,553.356 2205.31,435.812 2205.99,431.411 2206.66,590.793 2207.34,435.058 2208.02,509.116 2208.69,276.404 2209.37,528.78 2210.05,572.937 2210.72,409.669 \n",
       "  2211.4,690.785 2212.08,555.146 2212.75,693.279 2213.43,762.977 2214.1,769.922 2214.78,908.598 2215.46,528.977 2216.13,483.63 2216.81,342.385 2217.49,245.137 \n",
       "  2218.16,286.144 2218.84,289.025 2219.52,340.84 2220.19,230.004 2220.87,201.293 2221.55,294.158 2222.22,348.887 2222.9,666.676 2223.57,760.715 2224.25,853.972 \n",
       "  2224.93,680.093 2225.6,785.114 2226.28,780.383 2226.96,394.219 2227.63,560.521 2228.31,225.118 2228.99,418.13 2229.66,353.088 2230.34,235.755 2231.02,386.906 \n",
       "  2231.69,433.393 2232.37,510.635 2233.05,336.441 2233.72,171.856 2234.4,276.117 2235.07,380.093 2235.75,293.776 2236.43,402.218 2237.1,358.003 2237.78,464.343 \n",
       "  2238.46,157.149 2239.13,393.74 2239.81,277.512 2240.49,514.218 2241.16,494.054 2241.84,492.004 2242.52,327.315 2243.19,977.783 2243.87,734.368 2244.54,599.455 \n",
       "  2245.22,448.259 2245.9,332.364 2246.57,325.279 2247.25,383.495 2247.93,421.231 2248.6,383.321 2249.28,267.259 2249.96,492.244 2250.63,339.5 2251.31,675.65 \n",
       "  2251.99,643.058 2252.66,574.895 2253.34,602.487 2254.02,469.983 2254.69,567.967 2255.37,763.106 2256.04,242.602 2256.72,296.849 2257.4,184.574 2258.07,425.777 \n",
       "  2258.75,486.622 2259.43,360.209 2260.1,377.204 2260.78,463.97 2261.46,672.544 2262.13,549.741 2262.81,676.291 2263.49,304.842 2264.16,243.265 2264.84,512.097 \n",
       "  2265.51,622.624 2266.19,313.849 2266.87,270.679 2267.54,334.486 2268.22,369.897 2268.9,276.28 2269.57,370.867 2270.25,233.975 2270.93,431.337 2271.6,389.535 \n",
       "  2272.28,437.028 2272.96,560.535 2273.63,223.408 2274.31,507.82 2274.98,416.761 2275.66,415.331 2276.34,693.171 2277.01,620.172 2277.69,808.24 2278.37,403.791 \n",
       "  2279.04,372.559 2279.72,442.841 2280.4,616.257 2281.07,509.556 2281.75,493.938 2282.43,567.015 2283.1,306.863 2283.78,286.273 2284.46,188.864 2285.13,186.681 \n",
       "  2285.81,191.006 2286.48,311.67 2287.16,160.53 2287.84,286.681 2288.51,480.529 2289.19,324.395 2289.87,427.539 2290.54,629.364 2291.22,257.556 2291.9,414.278 \n",
       "  \n",
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       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Configure the stratigraphic Monte Carlo model\n",
    "config = NewStratAgeModelConfiguration()\n",
    "# If in doubt, you can probably leave these parameters as-is\n",
    "config.resolution = 0.2 # Same units as sample height. Smaller is slower!\n",
    "config.bounding = 0.5 # how far away do we place runaway bounds, as a fraction of total section height\n",
    "(bottom, top) = extrema(smpl.Height)\n",
    "npoints_approx = round(Int,length(bottom:config.resolution:top) * (1 + 2*config.bounding))\n",
    "config.nsteps = 3000 # Number of steps to run in distribution MCMC\n",
    "config.burnin = 2000*npoints_approx # Number to discard\n",
    "config.sieve = round(Int,npoints_approx) # Record one out of every nsieve steps\n",
    "\n",
    "# Run the stratigraphic MCMC model\n",
    "(mdl, agedist, lldist) = StratMetropolis14C(smpl, config)\n",
    "\n",
    "# Write the results to file\n",
    "run(`mkdir -p $(smpl.Path)`) # Make sure that the path exists\n",
    "writedlm(smpl.Path*\"agedist.csv\", agedist, ',') # Stationary distribution of the age-depth model\n",
    "writedlm(smpl.Path*\"height.csv\", mdl.Height, ',') # Stratigraphic heights corresponding to each row of agedist\n",
    "writedlm(smpl.Path*\"lldist.csv\", lldist, ',') # Log likelihood distribution (to check for stationarity)\n",
    "\n",
    "# Plot the log likelihood to make sure we're converged (n.b burnin isn't recorded)\n",
    "hdl = plot(lldist,xlabel=\"Step number\",ylabel=\"Log likelihood\",label=\"\",line=(0.85,:darkblue))\n",
    "savefig(hdl,smpl.Path*\"lldist.pdf\")\n",
    "display(hdl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Plot results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "  1559.99,1337.13 1547.99,1332.52 1529.77,1327.92 1527.23,1323.32 1512.52,1318.71 1500.74,1314.11 1491.25,1309.51 1484.96,1304.9 1463.46,1300.3 1451.66,1295.7 \n",
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       "  1167.23,1153 1161.22,1148.4 1155.81,1143.8 1148.84,1139.2 1142.66,1134.59 1139.72,1129.99 1127.64,1125.39 1122.39,1120.78 1120.72,1116.18 1120.58,1111.58 \n",
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       "  1071.26,1060.94 1065.01,1056.34 1061.01,1051.74 1050.75,1047.14 1045.08,1042.53 1038.3,1037.93 1028.74,1033.33 1020.83,1028.72 1015.63,1024.12 1009.42,1019.52 \n",
       "  1002.41,1014.91 983.967,1010.31 969.755,1005.71 955.108,1001.11 946.418,996.502 937.133,991.899 926.648,987.296 914.21,982.693 913.079,978.09 911.898,973.487 \n",
       "  898.992,968.884 888.106,964.281 873.43,959.678 869.273,955.075 859.609,950.472 854.794,945.869 854.208,941.266 843.753,936.663 840.256,932.06 839.334,927.457 \n",
       "  837.708,922.854 832.972,918.251 822.788,913.648 816.083,909.045 812.395,904.442 808.179,899.839 806.161,895.236 804.446,890.633 802.765,886.03 798.704,881.427 \n",
       "  789.907,876.823 788.932,872.22 783.759,867.617 779.081,863.014 772.996,858.411 768.637,853.808 765.207,849.205 765.066,844.602 751.315,839.999 747.515,835.396 \n",
       "  741.221,830.793 738.268,826.19 738.041,821.587 737.732,816.984 731.825,812.381 731.423,807.778 727.872,803.175 724.837,798.572 723.912,793.969 721.893,789.366 \n",
       "  716.704,784.763 716.508,780.16 713.366,775.557 713.366,770.954 712.659,766.351 711.32,761.748 707.905,757.145 702.568,752.542 698.819,747.939 696.289,743.336 \n",
       "  695.908,738.733 695.508,734.13 694.96,729.527 692.935,724.924 691.638,720.321 690.722,715.718 689.079,711.115 683.573,706.512 681.069,701.909 678.304,697.306 \n",
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       "  634.941,646.672 631.383,642.069 626.996,637.466 625.693,632.863 621.092,628.26 615.76,623.657 612.705,619.054 607.348,614.451 604.265,609.848 602.679,605.245 \n",
       "  599.936,600.642 592.084,596.039 579.269,591.436 576.126,586.833 572.926,582.23 568.919,577.627 566.896,573.024 562.23,568.421 560.151,563.818 559.031,559.215 \n",
       "  556.741,554.612 552.643,550.009 547.996,545.406 547.283,540.803 544.844,536.2 542.779,531.597 539.242,526.994 535.146,522.391 529.031,517.788 524.636,513.185 \n",
       "  523.792,508.582 523.734,503.979 521.686,499.376 520.18,494.773 519.354,490.17 518.278,485.567 518.244,480.964 514.869,476.361 514.731,471.758 513.719,467.155 \n",
       "  513.059,462.552 513.031,457.949 512.366,453.346 509.526,448.743 504.239,444.14 502.726,439.537 502.079,434.934 501.305,430.33 499.239,425.727 497.259,421.124 \n",
       "  496.068,416.521 494.351,411.918 494.184,407.315 492.313,402.712 491.936,398.109 490.46,393.506 489.722,388.903 486.676,384.3 486.047,379.697 484.397,375.094 \n",
       "  483.327,370.491 482.385,365.888 481.9,361.285 479.098,356.682 476.71,352.079 475.764,347.476 471.402,342.873 470.657,338.27 469.613,333.667 468.504,329.064 \n",
       "  467.151,324.461 465.271,319.858 462.031,315.255 459.819,310.652 457.334,306.049 454.99,301.446 449.776,296.843 445.534,292.24 445.534,287.637 443.365,283.034 \n",
       "  443.111,278.431 441.448,273.828 439.845,269.225 438.444,264.622 437.765,260.019 436.081,255.416 435.36,250.813 434.809,246.21 434.802,241.607 434.551,237.004 \n",
       "  434.39,232.401 433.904,227.798 432.772,223.195 431.815,218.592 431.674,213.989 431.564,209.385 430.978,204.782 430.085,200.179 429.898,195.576 429.669,190.973 \n",
       "  427.898,186.37 425.992,181.767 425.06,177.164 424.317,172.561 423.351,167.958 422.749,163.355 422.21,158.752 422.055,154.149 419.575,149.546 419.013,144.943 \n",
       "  418.998,140.34 418.617,135.737 418.214,131.134 417.986,126.531 417.652,121.928 417.641,117.325 416.866,112.722 416.701,108.119 415.685,103.516 415.119,98.913 \n",
       "  414.327,94.31 413.804,89.707 802.964,89.707 805.024,94.31 809.898,98.913 812.777,103.516 814.947,108.119 819.192,112.722 823.933,117.325 828.36,121.928 \n",
       "  838.185,126.531 842.635,131.134 844.696,135.737 846.807,140.34 853.534,144.943 858.524,149.546 862.481,154.149 867.431,158.752 872.024,163.355 879.149,167.958 \n",
       "  882.306,172.561 884.922,177.164 888.768,181.767 893.186,186.37 901.933,190.973 909.492,195.576 917.427,200.179 923.068,204.782 927.148,209.385 929.077,213.989 \n",
       "  939.218,218.592 944.368,223.195 947.43,227.798 952.25,232.401 957.868,237.004 959.456,241.607 963.883,246.21 970.194,250.813 972.193,255.416 979.627,260.019 \n",
       "  980.707,264.622 982.639,269.225 984.63,273.828 989.327,278.431 993.792,283.034 999.139,287.637 1004.42,292.24 1009.98,296.843 1010.28,301.446 1010.97,306.049 \n",
       "  1017.16,310.652 1022.13,315.255 1022.13,319.858 1025.47,324.461 1027.87,329.064 1031.74,333.667 1033.62,338.27 1035.74,342.873 1038.59,347.476 1038.68,352.079 \n",
       "  1039.87,356.682 1042.41,361.285 1042.56,365.888 1043.96,370.491 1044.49,375.094 1044.49,379.697 1049,384.3 1049.11,388.903 1054.57,393.506 1055.57,398.109 \n",
       "  1055.57,402.712 1058.2,407.315 1063.29,411.918 1069.18,416.521 1069.83,421.124 1070.17,425.727 1073.79,430.33 1074.19,434.934 1075.61,439.537 1077.26,444.14 \n",
       "  1077.26,448.743 1077.64,453.346 1078.04,457.949 1081.35,462.552 1083.34,467.155 1085.67,471.758 1093.67,476.361 1095.46,480.964 1096.02,485.567 1098.77,490.17 \n",
       "  1103.04,494.773 1103.04,499.376 1104.15,503.979 1109.43,508.582 1110.02,513.185 1115.17,517.788 1117.09,522.391 1117.09,526.994 1119.25,531.597 1120.89,536.2 \n",
       "  1121.56,540.803 1122.97,545.406 1125.38,550.009 1125.38,554.612 1126.96,559.215 1128.39,563.818 1128.95,568.421 1129.39,573.024 1130.33,577.627 1133.96,582.23 \n",
       "  1135.06,586.833 1140.42,591.436 1141.22,596.039 1143.37,600.642 1144.48,605.245 1144.8,609.848 1147.52,614.451 1149.17,619.054 1151.3,623.657 1151.67,628.26 \n",
       "  1154.28,632.863 1155.37,637.466 1160.26,642.069 1162.27,646.672 1163.41,651.275 1170.07,655.878 1174.07,660.482 1190.1,665.085 1197.06,669.688 1210.3,674.291 \n",
       "  1216.11,678.894 1242.84,683.497 1265.47,688.1 1272.59,692.703 1285.42,697.306 1291.94,701.909 1303.89,706.512 1313.63,711.115 1318.94,715.718 1330.62,720.321 \n",
       "  1337.49,724.924 1350.95,729.527 1354.05,734.13 1359.55,738.733 1369.3,743.336 1375.31,747.939 1381.04,752.542 1396.55,757.145 1400.34,761.748 1404.09,766.351 \n",
       "  1408.98,770.954 1418.87,775.557 1426.71,780.16 1433.95,784.763 1439.68,789.366 1442.37,793.969 1445.14,798.572 1446.03,803.175 1449.33,807.778 1453.18,812.381 \n",
       "  1455.26,816.984 1463.71,821.587 1466.72,826.19 1469.47,830.793 1472.52,835.396 1475.25,839.999 1477.7,844.602 1480.37,849.205 1483.4,853.808 1484.66,858.411 \n",
       "  1488.94,863.014 1489.81,867.617 1492.32,872.22 1503.76,876.823 1508,881.427 1510.46,886.03 1512.58,890.633 1517.35,895.236 1520.22,899.839 1522.76,904.442 \n",
       "  1523.37,909.045 1525.63,913.648 1525.65,918.251 1530.68,922.854 1533.23,927.457 1533.4,932.06 1534.93,936.663 1536.53,941.266 1539.58,945.869 1540.13,950.472 \n",
       "  1543.76,955.075 1544.47,959.678 1546.4,964.281 1548.17,968.884 1550.8,973.487 1552.94,978.09 1555.16,982.693 1556.33,987.296 1558.48,991.899 1560.4,996.502 \n",
       "  1560.68,1001.11 1561.42,1005.71 1562.75,1010.31 1564.08,1014.91 1566.56,1019.52 1568.09,1024.12 1568.99,1028.72 1569.42,1033.33 1571.63,1037.93 1572.3,1042.53 \n",
       "  1574.44,1047.14 1576.58,1051.74 1599.68,1056.34 1656.71,1060.94 1699.17,1065.55 1727.27,1070.15 1755.55,1074.75 1782.06,1079.36 1796.54,1083.96 1805.09,1088.56 \n",
       "  1829.44,1093.17 1845.87,1097.77 1865.14,1102.37 1890.71,1106.97 1911.5,1111.58 1926.38,1116.18 1936.81,1120.78 1951.45,1125.39 1962.98,1129.99 1973.7,1134.59 \n",
       "  1983.57,1139.2 1996.29,1143.8 2009.2,1148.4 2020.94,1153 2031.97,1157.61 2043.74,1162.21 2045.64,1166.81 2055.9,1171.42 2065.53,1176.02 2069.92,1180.62 \n",
       "  2076.57,1185.23 2087.78,1189.83 2095.71,1194.43 2098,1199.03 2108.22,1203.64 2115.33,1208.24 2131.12,1212.84 2135.13,1217.45 2136.63,1222.05 2143.4,1226.65 \n",
       "  2148.44,1231.26 2152.33,1235.86 2156.6,1240.46 2160.69,1245.07 2163.67,1249.67 2176.59,1254.27 2178.96,1258.87 2182.04,1263.48 2184.15,1268.08 2187.97,1272.68 \n",
       "  2194.54,1277.29 2200.35,1281.89 2202.71,1286.49 2206.9,1291.1 2207.62,1295.7 2210.09,1300.3 2216.66,1304.9 2217.18,1309.51 2217.95,1314.11 2220.5,1318.71 \n",
       "  2223.7,1323.32 2227.03,1327.92 2227.89,1332.52 2228.95,1337.13 2231.21,1341.73 2236.54,1346.33 2238.39,1350.93 2240.4,1355.54 2242.27,1360.14 2242.77,1364.74 \n",
       "  2245.22,1369.35 2249.15,1373.95 2251.22,1378.55 2253.9,1383.16 2253.9,1375.1 2251.22,1375.1 2249.15,1375.1 2245.22,1375.1 2242.77,1375.1 2242.27,1375.1 \n",
       "  2240.4,1375.1 2238.39,1375.1 2236.54,1375.1 2231.21,1375.1 2228.95,1375.1 2227.89,1375.1 2227.03,1375.1 2223.7,1375.1 2220.5,1375.1 2217.95,1375.1 \n",
       "  2217.18,1375.1 2216.66,1375.1 2210.09,1375.1 2207.62,1375.1 2206.9,1375.1 2202.71,1375.1 2200.35,1375.1 2194.54,1375.1 2187.97,1375.1 2184.15,1375.1 \n",
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     "output_type": "display_data"
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   ],
   "source": [
    "# Plot results (mean and 95% confidence interval for both model and data)\n",
    "hdl = plot([mdl.Age_025CI; reverse(mdl.Age_975CI)],[mdl.Height; reverse(mdl.Height)], fill=(minimum(mdl.Height),0.5,:blue), label=\"model\")\n",
    "plot!(hdl, mdl.Age, mdl.Height, linecolor=:blue, label=\"\")\n",
    "plot!(hdl, smpl.Age, smpl.Height, xerror=(smpl.Age-smpl.Age_025CI,smpl.Age_975CI-smpl.Age),label=\"data\",seriestype=:scatter,color=:black)\n",
    "plot!(hdl, xlabel=\"Age ($(smpl.Age_Unit))\", ylabel=\"Height ($(smpl.Height_Unit))\")\n",
    "savefig(hdl,smpl.Path*\"AgeDepthModel.svg\")\n",
    "savefig(hdl,smpl.Path*\"AgeDepthModel.pdf\")\n",
    "display(hdl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interpolated age at height=-404: 8213.878377486633 +145.27607341744988/-152.82619915759005 Years BP"
     ]
    },
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# Stratigraphic height at which to interpolate\n",
    "height = -404\n",
    "\n",
    "age_at_height = linterp1s(mdl.Height,mdl.Age,height)\n",
    "age_at_height_min = linterp1s(mdl.Height,mdl.Age_025CI,height)\n",
    "age_at_height_max = linterp1s(mdl.Height,mdl.Age_975CI,height)\n",
    "print(\"Interpolated age at height=$height: $age_at_height +$(age_at_height_max-age_at_height)/-$(age_at_height-age_at_height_min) $(smpl.Age_Unit)\")\n",
    "\n",
    "# Optional: interpolate full age distribution\n",
    "interpolated_distribution = Array{Float64}(undef,size(agedist,2))\n",
    "for i=1:size(agedist,2)\n",
    "    interpolated_distribution[i] = linterp1s(mdl.Height,agedist[:,i],height)\n",
    "end\n",
    "hdl = histogram(interpolated_distribution, nbins=50, fill=(0.75,:darkblue), label=\"\")\n",
    "plot!(hdl, xlabel=\"Age ($(smpl.Age_Unit)) at height=$height\", ylabel=\"Likelihood (unnormalized)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are other things we can plot as well, such as deposition rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "  1250.24,929.131 1297.64,942.276 1345.04,943.193 1392.44,948.536 1439.84,942.27 1487.24,943.843 1534.64,951.107 1582.04,965.729 1629.43,986.3 1676.83,1007.42 \n",
       "  1724.23,1026.05 1771.63,1045.53 1819.03,1068.55 1866.43,1089.77 1913.83,1114.72 1961.23,1132.37 2008.63,1141.32 2056.03,1144.54 2103.43,1142.25 2150.83,1142.29 \n",
       "  2198.23,1143.55 2245.63,1141.9 2293.03,1145.36 \n",
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       "  776.238,1119.91 823.638,1131.48 871.038,1156.76 918.438,1175.26 965.838,1190.66 1013.24,1202.67 1060.64,1214.04 1108.04,1224.1 1155.44,1225.79 1202.84,1232.15 \n",
       "  1250.24,1235.52 1297.64,1244.56 1345.04,1246.08 1392.44,1252.83 1439.84,1252.41 1487.24,1246.94 1534.64,1250.52 1582.04,1259.28 1629.43,1277.12 1676.83,1285.94 \n",
       "  1724.23,1294.67 1771.63,1299.45 1819.03,1307.44 1866.43,1316.04 1913.83,1319.06 1961.23,1324.42 2008.63,1333.5 2056.03,1338.15 2103.43,1339.81 2150.83,1345.01 \n",
       "  2198.23,1348.4 2245.63,1348.79 2293.03,1351.68 2293.03,998.24 2245.63,988.376 2198.23,983.056 2150.83,977.139 2103.43,979.77 2056.03,978.29 2008.63,976.262 \n",
       "  1961.23,962.607 1913.83,930.861 1866.43,880.004 1819.03,846.951 1771.63,811.865 1724.23,768.738 1676.83,738.02 1629.43,689.413 1582.04,665.747 1534.64,640.724 \n",
       "  1487.24,643.449 1439.84,640.063 1392.44,649.198 1345.04,643.184 1297.64,646.15 1250.24,623.591 1202.84,593.165 1155.44,563.529 1108.04,508.405 1060.64,464.871 \n",
       "  1013.24,402.449 965.838,312.46 918.438,241.841 871.038,165.923 823.638,132.617 776.238,129 728.838,125.877 681.439,108.215 634.039,95.6791 586.639,86.2547 \n",
       "  539.239,91.5002 491.839,92.498 444.44,108.873 397.04,166.274 349.64,185.094 302.24,207.294 302.24,1386.61 349.64,1386.61 397.04,1386.61 444.44,1386.61 \n",
       "  491.839,1386.61 539.239,1386.61 586.639,1386.61 634.039,1386.61 681.439,1386.61 728.838,1386.61 776.238,1386.61 823.638,1386.61 871.038,1386.61 918.438,1386.61 \n",
       "  965.838,1386.61 1013.24,1386.61 1060.64,1386.61 1108.04,1386.61 1155.44,1386.61 1202.84,1386.61 1250.24,1386.61 1297.64,1386.61 1345.04,1386.61 1392.44,1386.61 \n",
       "  1439.84,1386.61 1487.24,1386.61 1534.64,1386.61 1582.04,1386.61 1629.43,1386.61 1676.83,1386.61 1724.23,1386.61 1771.63,1386.61 1819.03,1386.61 1866.43,1386.61 \n",
       "  1913.83,1386.61 1961.23,1386.61 2008.63,1386.61 2056.03,1386.61 2103.43,1386.61 2150.83,1386.61 2198.23,1386.61 2245.63,1386.61 2293.03,1386.61 2293.03,1386.61 \n",
       "  2245.63,1386.61 2198.23,1386.61 2150.83,1386.61 2103.43,1386.61 2056.03,1386.61 2008.63,1386.61 1961.23,1386.61 1913.83,1386.61 1866.43,1386.61 1819.03,1386.61 \n",
       "  1771.63,1386.61 1724.23,1386.61 1676.83,1386.61 1629.43,1386.61 1582.04,1386.61 1534.64,1386.61 1487.24,1386.61 1439.84,1386.61 1392.44,1386.61 1345.04,1386.61 \n",
       "  1297.64,1386.61 1250.24,1386.61 1202.84,1386.61 1155.44,1386.61 1108.04,1386.61 1060.64,1386.61 1013.24,1386.61 965.838,1386.61 918.438,1386.61 871.038,1386.61 \n",
       "  823.638,1386.61 776.238,1386.61 728.838,1386.61 681.439,1386.61 634.039,1386.61 586.639,1386.61 539.239,1386.61 491.839,1386.61 444.44,1386.61 397.04,1386.61 \n",
       "  349.64,1386.61 302.24,1386.61 \n",
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       "  302.24,1143.99 349.64,1125.15 397.04,1118.09 444.44,1101.56 491.839,1079.39 539.239,1062.44 586.639,1072.88 634.039,1084.75 681.439,1101.45 728.838,1115.21 \n",
       "  776.238,1119.91 823.638,1131.48 871.038,1156.76 918.438,1175.26 965.838,1190.66 1013.24,1202.67 1060.64,1214.04 1108.04,1224.1 1155.44,1225.79 1202.84,1232.15 \n",
       "  1250.24,1235.52 1297.64,1244.56 1345.04,1246.08 1392.44,1252.83 1439.84,1252.41 1487.24,1246.94 1534.64,1250.52 1582.04,1259.28 1629.43,1277.12 1676.83,1285.94 \n",
       "  1724.23,1294.67 1771.63,1299.45 1819.03,1307.44 1866.43,1316.04 1913.83,1319.06 1961.23,1324.42 2008.63,1333.5 2056.03,1338.15 2103.43,1339.81 2150.83,1345.01 \n",
       "  2198.23,1348.4 2245.63,1348.79 2293.03,1351.68 2293.03,998.24 2245.63,988.376 2198.23,983.056 2150.83,977.139 2103.43,979.77 2056.03,978.29 2008.63,976.262 \n",
       "  1961.23,962.607 1913.83,930.861 1866.43,880.004 1819.03,846.951 1771.63,811.865 1724.23,768.738 1676.83,738.02 1629.43,689.413 1582.04,665.747 1534.64,640.724 \n",
       "  1487.24,643.449 1439.84,640.063 1392.44,649.198 1345.04,643.184 1297.64,646.15 1250.24,623.591 1202.84,593.165 1155.44,563.529 1108.04,508.405 1060.64,464.871 \n",
       "  1013.24,402.449 965.838,312.46 918.438,241.841 871.038,165.923 823.638,132.617 776.238,129 728.838,125.877 681.439,108.215 634.039,95.6791 586.639,86.2547 \n",
       "  539.239,91.5002 491.839,92.498 444.44,108.873 397.04,166.274 349.64,185.094 302.24,207.294 \n",
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       "  776.238,1066.47 823.638,1083.66 871.038,1107.19 918.438,1132.62 965.838,1150.87 1013.24,1166.13 1060.64,1176.26 1108.04,1185.81 1155.44,1187.49 1202.84,1197.32 \n",
       "  1250.24,1206.07 1297.64,1215.91 1345.04,1211.57 1392.44,1216.18 1439.84,1216.79 1487.24,1209.24 1534.64,1216.34 1582.04,1226.78 1629.43,1248.64 1676.83,1260.99 \n",
       "  1724.23,1268.01 1771.63,1272.68 1819.03,1281.45 1866.43,1294.57 1913.83,1299.46 1961.23,1303.87 2008.63,1312.83 2056.03,1319.14 2103.43,1321.24 2150.83,1328.02 \n",
       "  2198.23,1332.35 2245.63,1333.61 2293.03,1338.33 2293.03,1033.38 2245.63,1025.2 2198.23,1024.44 2150.83,1016.17 2103.43,1014.02 2056.03,1017.56 2008.63,1010.89 \n",
       "  1961.23,999.239 1913.83,969.399 1866.43,929.846 1819.03,898.806 1771.63,864.738 1724.23,826.968 1676.83,791.206 1629.43,758.672 1582.04,726.321 1534.64,705.505 \n",
       "  1487.24,694.349 1439.84,687.474 1392.44,708.436 1345.04,701.153 1297.64,696.545 1250.24,685.979 1202.84,657.977 1155.44,623.689 1108.04,593.921 1060.64,543.792 \n",
       "  1013.24,485.458 965.838,414.324 918.438,330.796 871.038,272.246 823.638,222.349 776.238,205.651 728.838,197.667 681.439,190.873 634.039,168.822 586.639,158.378 \n",
       "  539.239,175.684 491.839,179.789 444.44,192.669 397.04,239.596 349.64,265.204 302.24,279.043 302.24,1386.61 349.64,1386.61 397.04,1386.61 444.44,1386.61 \n",
       "  491.839,1386.61 539.239,1386.61 586.639,1386.61 634.039,1386.61 681.439,1386.61 728.838,1386.61 776.238,1386.61 823.638,1386.61 871.038,1386.61 918.438,1386.61 \n",
       "  965.838,1386.61 1013.24,1386.61 1060.64,1386.61 1108.04,1386.61 1155.44,1386.61 1202.84,1386.61 1250.24,1386.61 1297.64,1386.61 1345.04,1386.61 1392.44,1386.61 \n",
       "  1439.84,1386.61 1487.24,1386.61 1534.64,1386.61 1582.04,1386.61 1629.43,1386.61 1676.83,1386.61 1724.23,1386.61 1771.63,1386.61 1819.03,1386.61 1866.43,1386.61 \n",
       "  1913.83,1386.61 1961.23,1386.61 2008.63,1386.61 2056.03,1386.61 2103.43,1386.61 2150.83,1386.61 2198.23,1386.61 2245.63,1386.61 2293.03,1386.61 2293.03,1386.61 \n",
       "  2245.63,1386.61 2198.23,1386.61 2150.83,1386.61 2103.43,1386.61 2056.03,1386.61 2008.63,1386.61 1961.23,1386.61 1913.83,1386.61 1866.43,1386.61 1819.03,1386.61 \n",
       "  1771.63,1386.61 1724.23,1386.61 1676.83,1386.61 1629.43,1386.61 1582.04,1386.61 1534.64,1386.61 1487.24,1386.61 1439.84,1386.61 1392.44,1386.61 1345.04,1386.61 \n",
       "  1297.64,1386.61 1250.24,1386.61 1202.84,1386.61 1155.44,1386.61 1108.04,1386.61 1060.64,1386.61 1013.24,1386.61 965.838,1386.61 918.438,1386.61 871.038,1386.61 \n",
       "  823.638,1386.61 776.238,1386.61 728.838,1386.61 681.439,1386.61 634.039,1386.61 586.639,1386.61 539.239,1386.61 491.839,1386.61 444.44,1386.61 397.04,1386.61 \n",
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       "  302.24,1086.14 349.64,1055.08 397.04,1050.87 444.44,1031.53 491.839,1004.94 539.239,1002.32 586.639,1005.27 634.039,1023.97 681.439,1044.23 728.838,1057.85 \n",
       "  776.238,1066.47 823.638,1083.66 871.038,1107.19 918.438,1132.62 965.838,1150.87 1013.24,1166.13 1060.64,1176.26 1108.04,1185.81 1155.44,1187.49 1202.84,1197.32 \n",
       "  1250.24,1206.07 1297.64,1215.91 1345.04,1211.57 1392.44,1216.18 1439.84,1216.79 1487.24,1209.24 1534.64,1216.34 1582.04,1226.78 1629.43,1248.64 1676.83,1260.99 \n",
       "  1724.23,1268.01 1771.63,1272.68 1819.03,1281.45 1866.43,1294.57 1913.83,1299.46 1961.23,1303.87 2008.63,1312.83 2056.03,1319.14 2103.43,1321.24 2150.83,1328.02 \n",
       "  2198.23,1332.35 2245.63,1333.61 2293.03,1338.33 2293.03,1033.38 2245.63,1025.2 2198.23,1024.44 2150.83,1016.17 2103.43,1014.02 2056.03,1017.56 2008.63,1010.89 \n",
       "  1961.23,999.239 1913.83,969.399 1866.43,929.846 1819.03,898.806 1771.63,864.738 1724.23,826.968 1676.83,791.206 1629.43,758.672 1582.04,726.321 1534.64,705.505 \n",
       "  1487.24,694.349 1439.84,687.474 1392.44,708.436 1345.04,701.153 1297.64,696.545 1250.24,685.979 1202.84,657.977 1155.44,623.689 1108.04,593.921 1060.64,543.792 \n",
       "  1013.24,485.458 965.838,414.324 918.438,330.796 871.038,272.246 823.638,222.349 776.238,205.651 728.838,197.667 681.439,190.873 634.039,168.822 586.639,158.378 \n",
       "  539.239,175.684 491.839,179.789 444.44,192.669 397.04,239.596 349.64,265.204 302.24,279.043 \n",
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       "  776.238,1004.04 823.638,1024.84 871.038,1049.14 918.438,1083.12 965.838,1102.84 1013.24,1120.24 1060.64,1136.25 1108.04,1143.35 1155.44,1150.33 1202.84,1158.41 \n",
       "  1250.24,1169.87 1297.64,1179.14 1345.04,1179.8 1392.44,1179.73 1439.84,1173.32 1487.24,1171.31 1534.64,1178.85 1582.04,1189.62 1629.43,1210.43 1676.83,1222.17 \n",
       "  1724.23,1235.84 1771.63,1245.87 1819.03,1255.72 1866.43,1270.52 1913.83,1278.31 1961.23,1283.51 2008.63,1290.31 2056.03,1297.29 2103.43,1301.72 2150.83,1306.05 \n",
       "  2198.23,1312.49 2245.63,1315.23 2293.03,1320.61 2293.03,1069.25 2245.63,1061.56 2198.23,1059.75 2150.83,1054.13 2103.43,1049.16 2056.03,1052.77 2008.63,1047.02 \n",
       "  1961.23,1036.97 1913.83,1011.88 1866.43,972.572 1819.03,948.054 1771.63,916.916 1724.23,883.714 1676.83,849.851 1629.43,816.175 1582.04,787.747 1534.64,765.702 \n",
       "  1487.24,758.231 1439.84,751.419 1392.44,763.157 1345.04,760.856 1297.64,754.905 1250.24,745.693 1202.84,723.153 1155.44,703.449 1108.04,665.012 1060.64,623.234 \n",
       "  1013.24,568.297 965.838,499.497 918.438,434.018 871.038,366.047 823.638,329.738 776.238,300.686 728.838,301.209 681.439,289.236 634.039,266.398 586.639,259.066 \n",
       "  539.239,262.047 491.839,262.674 444.44,280.782 397.04,325.786 349.64,342.241 302.24,360.617 302.24,1386.61 349.64,1386.61 397.04,1386.61 444.44,1386.61 \n",
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       "  965.838,1386.61 1013.24,1386.61 1060.64,1386.61 1108.04,1386.61 1155.44,1386.61 1202.84,1386.61 1250.24,1386.61 1297.64,1386.61 1345.04,1386.61 1392.44,1386.61 \n",
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       "  2245.63,1386.61 2198.23,1386.61 2150.83,1386.61 2103.43,1386.61 2056.03,1386.61 2008.63,1386.61 1961.23,1386.61 1913.83,1386.61 1866.43,1386.61 1819.03,1386.61 \n",
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       "  823.638,1386.61 776.238,1386.61 728.838,1386.61 681.439,1386.61 634.039,1386.61 586.639,1386.61 539.239,1386.61 491.839,1386.61 444.44,1386.61 397.04,1386.61 \n",
       "  349.64,1386.61 302.24,1386.61 \n",
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       "  776.238,1004.04 823.638,1024.84 871.038,1049.14 918.438,1083.12 965.838,1102.84 1013.24,1120.24 1060.64,1136.25 1108.04,1143.35 1155.44,1150.33 1202.84,1158.41 \n",
       "  1250.24,1169.87 1297.64,1179.14 1345.04,1179.8 1392.44,1179.73 1439.84,1173.32 1487.24,1171.31 1534.64,1178.85 1582.04,1189.62 1629.43,1210.43 1676.83,1222.17 \n",
       "  1724.23,1235.84 1771.63,1245.87 1819.03,1255.72 1866.43,1270.52 1913.83,1278.31 1961.23,1283.51 2008.63,1290.31 2056.03,1297.29 2103.43,1301.72 2150.83,1306.05 \n",
       "  2198.23,1312.49 2245.63,1315.23 2293.03,1320.61 2293.03,1069.25 2245.63,1061.56 2198.23,1059.75 2150.83,1054.13 2103.43,1049.16 2056.03,1052.77 2008.63,1047.02 \n",
       "  1961.23,1036.97 1913.83,1011.88 1866.43,972.572 1819.03,948.054 1771.63,916.916 1724.23,883.714 1676.83,849.851 1629.43,816.175 1582.04,787.747 1534.64,765.702 \n",
       "  1487.24,758.231 1439.84,751.419 1392.44,763.157 1345.04,760.856 1297.64,754.905 1250.24,745.693 1202.84,723.153 1155.44,703.449 1108.04,665.012 1060.64,623.234 \n",
       "  1013.24,568.297 965.838,499.497 918.438,434.018 871.038,366.047 823.638,329.738 776.238,300.686 728.838,301.209 681.439,289.236 634.039,266.398 586.639,259.066 \n",
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     "text": [
      "  0.197671 seconds (600.74 k allocations: 54.665 MiB, 11.02% gc time)\n"
     ]
    }
   ],
   "source": [
    "# Set bin width and spacing\n",
    "binwidth = round(nanrange(mdl.Age)/10,sigdigits=1) # Can also set manually, commented out below\n",
    "# binwidth = 100 # Same units as smpl.Age\n",
    "binoverlap = 10\n",
    "ages = collect(minimum(mdl.Age):binwidth/binoverlap:maximum(mdl.Age))\n",
    "bincenters = ages[1+Int(binoverlap/2):end-Int(binoverlap/2)]\n",
    "spacing = binoverlap\n",
    "\n",
    "# Calculate rates for the stratigraphy of each markov chain step\n",
    "dhdt_dist = Array{Float64}(undef, length(ages)-binoverlap, config.nsteps)\n",
    "@time for i=1:config.nsteps\n",
    "    heights = linterp1(reverse(agedist[:,i]), reverse(mdl.Height), ages)\n",
    "    dhdt_dist[:,i] .= abs.(heights[1:end-spacing] - heights[spacing+1:end]) ./ binwidth\n",
    "end\n",
    "\n",
    "# Find mean and 1-sigma (68%) CI\n",
    "dhdt = nanmean(dhdt_dist,dim=2)\n",
    "dhdt_50p = nanmedian(dhdt_dist,dim=2)\n",
    "dhdt_16p = nanpctile(dhdt_dist,15.865,dim=2) # Minus 1-sigma (15.865th percentile)\n",
    "dhdt_84p = nanpctile(dhdt_dist,84.135,dim=2) # Plus 1-sigma (84.135th percentile)\n",
    "# Other confidence intervals (10:10:50)\n",
    "dhdt_20p = nanpctile(dhdt_dist,20,dim=2)\n",
    "dhdt_80p = nanpctile(dhdt_dist,80,dim=2)\n",
    "dhdt_25p = nanpctile(dhdt_dist,25,dim=2)\n",
    "dhdt_75p = nanpctile(dhdt_dist,75,dim=2)\n",
    "dhdt_30p = nanpctile(dhdt_dist,30,dim=2)\n",
    "dhdt_70p = nanpctile(dhdt_dist,70,dim=2)\n",
    "dhdt_35p = nanpctile(dhdt_dist,35,dim=2)\n",
    "dhdt_65p = nanpctile(dhdt_dist,65,dim=2)\n",
    "dhdt_40p = nanpctile(dhdt_dist,40,dim=2)\n",
    "dhdt_60p = nanpctile(dhdt_dist,60,dim=2)\n",
    "dhdt_45p = nanpctile(dhdt_dist,45,dim=2)\n",
    "dhdt_55p = nanpctile(dhdt_dist,55,dim=2)\n",
    "\n",
    "# Plot results\n",
    "hdl = plot(bincenters,dhdt, label=\"Mean\", color=:black, linewidth=2)\n",
    "plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_16p; reverse(dhdt_84p)], fill=(0,0.2,:darkblue), linealpha=0, label=\"68% CI\")\n",
    "plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_20p; reverse(dhdt_80p)], fill=(0,0.2,:darkblue), linealpha=0, label=\"\")\n",
    "plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_25p; reverse(dhdt_75p)], fill=(0,0.2,:darkblue), linealpha=0, label=\"\")\n",
    "plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_30p; reverse(dhdt_70p)], fill=(0,0.2,:darkblue), linealpha=0, label=\"\")\n",
    "plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_35p; reverse(dhdt_65p)], fill=(0,0.2,:darkblue), linealpha=0, label=\"\")\n",
    "plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_40p; reverse(dhdt_60p)], fill=(0,0.2,:darkblue), linealpha=0, label=\"\")\n",
    "plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_45p; reverse(dhdt_55p)], fill=(0,0.2,:darkblue), linealpha=0, label=\"\")\n",
    "plot!(hdl,bincenters,dhdt_50p, label=\"Median\", color=:grey, linewidth=1)\n",
    "plot!(hdl, xlabel=\"Age ($(smpl.Age_Unit))\", ylabel=\"Depositional Rate ($(smpl.Height_Unit) / $(smpl.Age_Unit) over $binwidth $(smpl.Age_Unit))\", fg_color_legend=:white)\n",
    "savefig(hdl,smpl.Path*\"DepositionRateModelCI.pdf\")\n",
    "display(hdl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Stratigraphic model including hiatuses\n",
    "We can also deal with discrete hiatuses in the stratigraphic section if we know where they are and about how long they lasted. We need some different models and methods though. In particular, in addition to the `ChronAgeData` struct, we also need a `HiatusData` struct now, and will have a new `hiatusdist` output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating stratigraphic age-depth model...\n",
      "Burn-in: 680000 steps\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBurn-in...100%|█████████████████████████████████████████| Time: 0:13:39\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting sieved stationary distribution: 1020000 steps\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mCollecting...100%|██████████████████████████████████████| Time: 0:21:35\u001b[39m\n"
     ]
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       "<g clip-path=\"url(#clip6400)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 233.245, 218.83)\" x=\"233.245\" y=\"218.83\">-360</text>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 89.2861, 736.431)\" x=\"89.2861\" y=\"736.431\">Height (m)</text>\n",
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       "  1673.14,1337.13 1666.58,1332.52 1662,1327.92 1653.32,1323.32 1647.09,1318.71 1643.28,1314.11 1629.3,1309.51 1618.87,1304.9 1608.96,1300.3 1594.76,1295.7 \n",
       "  1580.87,1291.1 1553.9,1286.49 1547.64,1281.89 1537,1277.29 1534.21,1272.68 1518.81,1268.08 1495.02,1263.48 1488.13,1258.87 1479.59,1254.27 1471.58,1249.67 \n",
       "  1460.72,1245.07 1422.1,1240.46 1237.68,1235.86 1230.4,1231.26 1225.48,1226.65 1213.08,1222.05 1203.24,1217.45 1198.65,1212.84 1192.1,1208.24 1188.89,1203.64 \n",
       "  1180.8,1199.03 1167.94,1194.43 1161.9,1189.83 1153.8,1185.23 1145.15,1180.62 1143.91,1176.02 1142.36,1171.42 1140.07,1166.81 1137.37,1162.21 1133.36,1157.61 \n",
       "  1126.82,1153 1124.28,1148.4 1116.55,1143.8 1105.41,1139.2 1102.63,1134.59 1097.93,1129.99 1097.75,1125.39 1092.98,1120.78 1087.49,1116.18 1083.23,1111.58 \n",
       "  1077.37,1106.97 1071.49,1102.37 1068.6,1097.77 1067.69,1093.17 1063.34,1088.56 1061.39,1083.96 1058.84,1079.36 1056.98,1074.75 1054.17,1070.15 1051.54,1065.55 \n",
       "  1051.34,1060.94 1045.22,1056.34 1043.54,1051.74 1036.25,1047.14 1027.24,1042.53 1016.46,1037.93 1015,1033.33 1004.75,1028.72 999.856,1024.12 988.547,1019.52 \n",
       "  985.113,1014.91 977.175,1010.31 967.386,1005.71 961.734,1001.11 959.176,996.502 955.508,991.899 951.584,987.296 932.01,982.693 922.841,978.09 918.816,973.487 \n",
       "  915.144,968.884 908.521,964.281 898.988,959.678 891.978,955.075 887.99,950.472 877.808,945.869 869.928,941.266 862.961,936.663 859.009,932.06 850.715,927.457 \n",
       "  847.418,922.854 841.17,918.251 831.133,913.648 829.901,909.045 829.115,904.442 824.276,899.839 814.942,895.236 812.045,890.633 802.797,886.03 795.286,881.427 \n",
       "  792.12,876.823 787.264,872.22 784.786,867.617 781.833,863.014 774.034,858.411 771.434,853.808 771.067,849.205 770.346,844.602 763.466,839.999 760.767,835.396 \n",
       "  751.992,830.793 746.512,826.19 740.271,821.587 734.099,816.984 731.174,812.381 728.591,807.778 727.624,803.175 726.051,798.572 723.703,793.969 722.536,789.366 \n",
       "  720.376,784.763 720.094,780.16 715.114,775.557 711.681,770.954 705.561,766.351 700.255,761.748 698.488,757.145 698.226,752.542 695.013,747.939 694.458,743.336 \n",
       "  694.458,738.733 690.478,734.13 687.338,729.527 686.389,724.924 683.753,720.321 681.636,715.718 680.766,711.115 678.387,706.512 676.337,701.909 673.575,697.306 \n",
       "  671.695,692.703 668.821,688.1 666.97,683.497 661.499,678.894 659.184,674.291 653.934,669.688 652.345,665.085 650.105,660.482 646.225,655.878 645.734,651.275 \n",
       "  641.521,646.672 637.659,642.069 634.291,637.466 629.169,632.863 621.025,628.26 616.621,623.657 607.217,619.054 603.112,614.451 599.991,609.848 596.78,605.245 \n",
       "  590.684,600.642 586.173,596.039 583.555,591.436 573.357,586.833 572.485,582.23 571.212,577.627 563.374,573.024 561.166,568.421 560.026,563.818 552.778,559.215 \n",
       "  551.44,554.612 549.841,550.009 547.612,545.406 547.201,540.803 542.104,536.2 539.704,531.597 537.945,526.994 533.966,522.391 529.948,517.788 528.353,513.185 \n",
       "  525.731,508.582 525.494,503.979 522.949,499.376 521.772,494.773 519.274,490.17 518.123,485.567 518.123,480.964 515.827,476.361 513.492,471.758 512.004,467.155 \n",
       "  504.233,462.552 500.686,457.949 498.889,453.346 498.019,448.743 495.964,444.14 491.485,439.537 490.673,434.934 489.048,430.33 488.233,425.727 487.121,421.124 \n",
       "  486.31,416.521 485.735,411.918 484.592,407.315 480.281,402.712 479.614,398.109 476.416,393.506 473.92,388.903 473.529,384.3 468.725,379.697 468.1,375.094 \n",
       "  464.896,370.491 464.649,365.888 462.608,361.285 460.72,356.682 460.176,352.079 458.939,347.476 458.603,342.873 457.792,338.27 454.872,333.667 452.934,329.064 \n",
       "  451.28,324.461 446.857,319.858 445.906,315.255 445.675,310.652 444.626,306.049 443.719,301.446 443.059,296.843 441.915,292.24 438.653,287.637 438.046,283.034 \n",
       "  437.574,278.431 436.363,273.828 434.415,269.225 434.415,264.622 434.223,260.019 434.223,255.416 433.21,250.813 432.431,246.21 431.801,241.607 430.613,237.004 \n",
       "  430.61,232.401 428.93,227.798 427.824,223.195 426.528,218.592 426.209,213.989 425.594,209.385 424.189,204.782 423.693,200.179 423.492,195.576 423.368,190.973 \n",
       "  422.559,186.37 422.338,181.767 422.338,177.164 421.745,172.561 421.702,167.958 421.204,163.355 419.927,158.752 418.666,154.149 418.609,149.546 418.149,144.943 \n",
       "  417.927,140.34 417.924,135.737 417.789,131.134 417.037,126.531 416.569,121.928 415.947,117.325 415.226,112.722 414.872,108.119 413.137,103.516 412.357,98.913 \n",
       "  412.281,94.31 412.232,89.707 807.379,89.707 811.217,94.31 818.757,98.913 820.677,103.516 829.264,108.119 830.555,112.722 831.353,117.325 836.704,121.928 \n",
       "  838.077,126.531 838.702,131.134 840.613,135.737 843.926,140.34 847.055,144.943 849.74,149.546 859.731,154.149 863.856,158.752 864.546,163.355 873.727,167.958 \n",
       "  875.28,172.561 875.801,177.164 877.196,181.767 879.731,186.37 889.044,190.973 894.568,195.576 902.785,200.179 904.154,204.782 908.475,209.385 915.141,213.989 \n",
       "  918.732,218.592 926.323,223.195 931.933,227.798 933.034,232.401 935.383,237.004 938.402,241.607 940.914,246.21 941.588,250.813 947.175,255.416 950.352,260.019 \n",
       "  951.48,264.622 958.966,269.225 964.146,273.828 970.679,278.431 973.579,283.034 977.367,287.637 978.904,292.24 981.873,296.843 983.835,301.446 990.133,306.049 \n",
       "  994.613,310.652 995.866,315.255 997.919,319.858 999.471,324.461 1003.18,329.064 1005.41,333.667 1015.9,338.27 1018.14,342.873 1018.25,347.476 1023.38,352.079 \n",
       "  1026.99,356.682 1028.47,361.285 1037.51,365.888 1037.62,370.491 1039.61,375.094 1042.42,379.697 1044.42,384.3 1047.54,388.903 1052.02,393.506 1053.04,398.109 \n",
       "  1053.04,402.712 1058.61,407.315 1061.62,411.918 1063.69,416.521 1070.71,421.124 1070.86,425.727 1070.86,430.33 1073.05,434.934 1073.43,439.537 1076.28,444.14 \n",
       "  1077.29,448.743 1077.69,453.346 1082.4,457.949 1083.89,462.552 1103.63,467.155 1105.48,471.758 1108.56,476.361 1108.7,480.964 1111.31,485.567 1112.01,490.17 \n",
       "  1112.01,494.773 1113.3,499.376 1113.3,503.979 1115.93,508.582 1116.21,513.185 1117.34,517.788 1117.41,522.391 1121.23,526.994 1123.83,531.597 1126.61,536.2 \n",
       "  1128.2,540.803 1128.74,545.406 1128.74,550.009 1128.85,554.612 1131.84,559.215 1134.68,563.818 1135.66,568.421 1135.84,573.024 1138.85,577.627 1141.45,582.23 \n",
       "  1142.32,586.833 1142.74,591.436 1150.24,596.039 1150.24,600.642 1150.62,605.245 1151.86,609.848 1152.24,614.451 1152.24,619.054 1153.2,623.657 1156.06,628.26 \n",
       "  1157.14,632.863 1160.06,637.466 1161.2,642.069 1163.63,646.672 1165.53,651.275 1165.64,655.878 1165.64,660.482 1176.8,665.085 1198.69,669.688 1209.84,674.291 \n",
       "  1224.72,678.894 1241.49,683.497 1270.57,688.1 1276.02,692.703 1282.13,697.306 1300.57,701.909 1310.5,706.512 1315.49,711.115 1324.52,715.718 1328.98,720.321 \n",
       "  1334.31,724.924 1339.33,729.527 1350.64,734.13 1356.69,738.733 1359.22,743.336 1364.89,747.939 1374.98,752.542 1381.41,757.145 1387.34,761.748 1388.88,766.351 \n",
       "  1392.63,770.954 1400.04,775.557 1416.66,780.16 1422.62,784.763 1428.06,789.366 1433.64,793.969 1439.63,798.572 1441.77,803.175 1446.56,807.778 1454.07,812.381 \n",
       "  1458.84,816.984 1465.89,821.587 1466.34,826.19 1469.32,830.793 1472.21,835.396 1475.51,839.999 1478.98,844.602 1482.98,849.205 1486.04,853.808 1488.6,858.411 \n",
       "  1493.85,863.014 1495.77,867.617 1496.08,872.22 1498.64,876.823 1500.12,881.427 1503.51,886.03 1506.34,890.633 1508.14,895.236 1510.88,899.839 1517.43,904.442 \n",
       "  1520.2,909.045 1520.2,913.648 1521.74,918.251 1523.09,922.854 1526.68,927.457 1530.36,932.06 1530.83,936.663 1532.47,941.266 1536.66,945.869 1539.4,950.472 \n",
       "  1539.4,955.075 1540.63,959.678 1541.41,964.281 1542.92,968.884 1545.33,973.487 1547.9,978.09 1548.05,982.693 1549.38,987.296 1550.81,991.899 1551.88,996.502 \n",
       "  1552.15,1001.11 1554.74,1005.71 1555.52,1010.31 1558.3,1014.91 1561.47,1019.52 1562.86,1024.12 1563.44,1028.72 1564.33,1033.33 1566.88,1037.93 1567.01,1042.53 \n",
       "  1568.42,1047.14 1568.79,1051.74 1581.77,1056.34 1605.19,1060.94 1623.42,1065.55 1642.2,1070.15 1658.18,1074.75 1676.53,1079.36 1696.06,1083.96 1713.46,1088.56 \n",
       "  1727.82,1093.17 1742.04,1097.77 1754.4,1102.37 1769.85,1106.97 1783.68,1111.58 1788.33,1116.18 1794.19,1120.78 1795.71,1125.39 1801.33,1129.99 1808.5,1134.59 \n",
       "  1817.93,1139.2 1822.95,1143.8 1830.47,1148.4 1838.38,1153 1847.02,1157.61 1860.67,1162.21 1866.08,1166.81 1874.39,1171.42 1885.86,1176.02 1890.83,1180.62 \n",
       "  1901.77,1185.23 1913.49,1189.83 1928.9,1194.43 1940.71,1199.03 1946.69,1203.64 1953.96,1208.24 1964.5,1212.84 1971.22,1217.45 1981.7,1222.05 1996.7,1226.65 \n",
       "  2006.65,1231.26 2018.23,1235.86 2194.62,1240.46 2201.82,1245.07 2204.46,1249.67 2208.28,1254.27 2211.87,1258.87 2220.36,1263.48 2222.5,1268.08 2223.37,1272.68 \n",
       "  2225.9,1277.29 2228.06,1281.89 2229.84,1286.49 2234.69,1291.1 2235.12,1295.7 2240,1300.3 2242.28,1304.9 2244.9,1309.51 2247.36,1314.11 2250.01,1318.71 \n",
       "  2252.53,1323.32 2253.74,1327.92 2254.52,1332.52 2255.04,1337.13 2256.04,1341.73 2256.45,1346.33 2256.72,1350.93 2257.17,1355.54 2258.12,1360.14 2258.58,1364.74 \n",
       "  2258.98,1369.35 2260.1,1373.95 2260.55,1378.55 2261.91,1383.16 2261.91,1383.16 2260.55,1383.16 2260.1,1383.16 2258.98,1383.16 2258.58,1383.16 2258.12,1383.16 \n",
       "  2257.17,1383.16 2256.72,1383.16 2256.45,1383.16 2256.04,1383.16 2255.04,1383.16 2254.52,1383.16 2253.74,1383.16 2252.53,1383.16 2250.01,1383.16 2247.36,1383.16 \n",
       "  2244.9,1383.16 2242.28,1383.16 2240,1383.16 2235.12,1383.16 2234.69,1383.16 2229.84,1383.16 2228.06,1383.16 2225.9,1383.16 2223.37,1383.16 2222.5,1383.16 \n",
       "  2220.36,1383.16 2211.87,1383.16 2208.28,1383.16 2204.46,1383.16 2201.82,1383.16 2194.62,1383.16 2018.23,1383.16 2006.65,1383.16 1996.7,1383.16 1981.7,1383.16 \n",
       "  1971.22,1383.16 1964.5,1383.16 1953.96,1383.16 1946.69,1383.16 1940.71,1383.16 1928.9,1383.16 1913.49,1383.16 1901.77,1383.16 1890.83,1383.16 1885.86,1383.16 \n",
       "  1874.39,1383.16 1866.08,1383.16 1860.67,1383.16 1847.02,1383.16 1838.38,1383.16 1830.47,1383.16 1822.95,1383.16 1817.93,1383.16 1808.5,1383.16 1801.33,1383.16 \n",
       "  1795.71,1383.16 1794.19,1383.16 1788.33,1383.16 1783.68,1383.16 1769.85,1383.16 1754.4,1383.16 1742.04,1383.16 1727.82,1383.16 1713.46,1383.16 1696.06,1383.16 \n",
       "  1676.53,1383.16 1658.18,1383.16 1642.2,1383.16 1623.42,1383.16 1605.19,1383.16 1581.77,1383.16 1568.79,1383.16 1568.42,1383.16 1567.01,1383.16 1566.88,1383.16 \n",
       "  1564.33,1383.16 1563.44,1383.16 1562.86,1383.16 1561.47,1383.16 1558.3,1383.16 1555.52,1383.16 1554.74,1383.16 1552.15,1383.16 1551.88,1383.16 1550.81,1383.16 \n",
       "  1549.38,1383.16 1548.05,1383.16 1547.9,1383.16 1545.33,1383.16 1542.92,1383.16 1541.41,1383.16 1540.63,1383.16 1539.4,1383.16 1539.4,1383.16 1536.66,1383.16 \n",
       "  1532.47,1383.16 1530.83,1383.16 1530.36,1383.16 1526.68,1383.16 1523.09,1383.16 1521.74,1383.16 1520.2,1383.16 1520.2,1383.16 1517.43,1383.16 1510.88,1383.16 \n",
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "config.nsteps = 3000 # Number of steps to run in distribution MCMC\n",
    "config.burnin = 2000*npoints_approx # Number to discard\n",
    "# Data about hiatuses\n",
    "nHiatuses = 2 # The number of hiatuses you have data for\n",
    "hiatus = NewHiatusData(nHiatuses) # Struct to hold data\n",
    "hiatus.Height         = [-371.5, -405.0 ]\n",
    "hiatus.Height_sigma   = [   0.0,    0.0 ]\n",
    "hiatus.Duration       = [ 100.0,   123.0]\n",
    "hiatus.Duration_sigma = [  30.5,    20.0]\n",
    "\n",
    "# Run the model. Note the new `hiatus` argument and `hiatusdist` result\n",
    "(mdl, agedist, hiatusdist, lldist) = StratMetropolis14C(smpl, hiatus, config); sleep(0.5)\n",
    "\n",
    "# Plot results (mean and 95% confidence interval for both model and data)\n",
    "hdl = plot([mdl.Age_025CI; reverse(mdl.Age_975CI)],[mdl.Height; reverse(mdl.Height)], fill=(minimum(mdl.Height),0.5,:blue), label=\"model\")\n",
    "plot!(hdl, mdl.Age, mdl.Height, linecolor=:blue, label=\"\", fg_color_legend=:white)\n",
    "plot!(hdl, smpl.Age, smpl.Height, xerror=(smpl.Age-smpl.Age_025CI,smpl.Age_975CI-smpl.Age),label=\"data\",seriestype=:scatter,color=:black)\n",
    "plot!(hdl, xlabel=\"Age ($(smpl.Age_Unit))\", ylabel=\"Height ($(smpl.Height_Unit))\")\n",
    "# savefig(hdl,smpl.Path*\"AgeDepthModelHiatus.pdf\");\n",
    "display(hdl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Getting your data out\n",
    "As shown below, we have access to the system command line, so we can use the unix command `ls` to see all the files we have written. We'll try this first using `;` to access Julia's command-line shell mode:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AgeDepthModel.pdf\n",
      "AgeDepthModel.svg\n",
      "AgeDepthModelHiatus.pdf\n",
      "DepositionRateModelCI.pdf\n",
      "agedist.csv\n",
      "height.csv\n",
      "lldist.csv\n",
      "lldist.pdf\n"
     ]
    }
   ],
   "source": [
    "; ls MyData"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we could do the same thing using the `run` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AgeDepthModel.pdf\n",
      "AgeDepthModel.svg\n",
      "AgeDepthModelHiatus.pdf\n",
      "DepositionRateModelCI.pdf\n",
      "agedist.csv\n",
      "height.csv\n",
      "lldist.csv\n",
      "lldist.pdf\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Process(`\u001b[4mls\u001b[24m \u001b[4mMyData\u001b[24m`, ProcessExited(0))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run(`ls MyData`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you're running this as an online notebook, getting these files out of here may be harder though. For SVG files, one option is to view them in markdown cells, which you should then be able to right click and download as real vector graphics. e.g. pasting something like\n",
    "```\n",
    "<img src=\"AgeDepthModel.svg\" align=\"left\" width=\"600\"/>\n",
    "```\n",
    "in a markdown cell such as this one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Meanwhile, for the csv files we could try something like `; cat agedist.csv`, but agedist is probably too big to print. Let's try using ffsend instead, which should give you a download link. In fact, while we're at it, we might as well archive and zip the entire directory!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make gzipped tar archive of the the whole MyData directory\n",
    "run(`tar -zcf archive.tar.gz ./MyData`);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
      "                                 Dload  Upload   Total   Spent    Left  Speed\n",
      "100   622    0   622    0     0   1718      0 --:--:-- --:--:-- --:--:--  1713\n",
      "100 10.8M  100 10.8M    0     0  3750k      0  0:00:02  0:00:02 --:--:-- 6418k\n"
     ]
    }
   ],
   "source": [
    "# Download prebuilt ffsend linux binary\n",
    "download(\"https://github.com/timvisee/ffsend/releases/download/v0.2.65/ffsend-v0.2.65-linux-x64-static\", \"ffsend\")\n",
    "\n",
    "# Make ffsend executable\n",
    "run(`chmod +x ffsend`);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "; ./ffsend upload archive.tar.gz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You could alternatively use the ffsend command in this way to transfer individual files, for instance `; ./ffsend upload MyData/agedist.csv`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keep in mind that any changes you make to this online notebook won't persist after you close the tab (or after it times out) even if you save your changes! You have to either copy-paste or `file`>`Download as` a copy.\n",
    "***\n",
    "[![DOI](https://raw.githubusercontent.com/brenhinkeller/Chron.jl/main/readme_figures/osf_io_TQX3F.svg?sanitize=true)](https://doi.org/10.17605/osf.io/TQX3F) "
   ]
  }
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