Plots_for_Bayesian_analyses.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# Demonstrating plot functions useful for Bayesian analyses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook demonstrates the use of the functions\n",
    "`smooth_histogram`, `density_contour`, and `density_contour_joint`\n",
    "in the package `flavio.plots`.\n",
    "These functions are particularly useful for Bayesian analyses using Markov chains where the marginal posterior distributions are obtained from high-dimensional posterior samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preliminaries: imports"
   ]
  },
  {
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   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "import flavio\n",
    "import flavio.plots\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "flavio.__version__, matplotlib.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating random data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we draw 1 million tuples from a bivariate normal distribution with unit variance and 50% correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = np.random.multivariate_normal(mean=[0,0], cov=[[1,0.5], [0.5,1]], size=1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x, y = r.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1D smooth histograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting a simple 1D histogram with a Gaussian kernel density estimator is as simple as calling `smooth_histogram(x)`. The shading corresponds to 68% probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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    "\n",
    "plt.hist(x, normed=True, bins=50, alpha=0.2, color='k', label='discrete histogram');\n",
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    "If the number of points is smaller - taking a mere 50 points for example - the result depends on the kernel bandwith used. The automatic choice leads to a nice Gaussian, while reducing the bandwidth follows more and more the discrete nature of the distribution."
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flavio.plots.smooth_histogram(x[:50], label='automatic bandwidth')\n",
    "flavio.plots.smooth_histogram(x[:50], bandwidth=0.2, fill=False, col=1, label='bandwidth 0.2')\n",
    "\n",
    "plt.hist(x[:50], normed=True, bins=50, alpha=0.2, color='k', label='discrete histogram');\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2D density contours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `density_contour` function is useful for 2D distributions. By default, it shows 1 and 2$\\sigma$ (68.3 and 95.5% probability) contours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
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   "source": [
    "plt.figure(figsize=(4,4))\n",
    "plt.scatter(x, y, label='scatter plot', rasterized=True, s=0.2, c='0.5', alpha=0.4)\n",
    "\n",
    "flavio.plots.density_contour(x, y, label='density contours')\n",
    "\n",
    "plt.legend()"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of contours can also be increased, but it depends on the statistics whether they are meaningful, as seen in this example for the $4\\sigma$ contour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
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       "L 104.321034 175.512271 \n",
       "L 105.442642 175.643202 \n",
       "L 105.820183 175.692161 \n",
       "z\n",
       "M 115.078377 153.838894 \n",
       "L 114.415506 153.594588 \n",
       "L 113.293898 153.134629 \n",
       "L 112.412117 152.746231 \n",
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       "L 102.738439 136.356281 \n",
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       "L 103.123366 134.170955 \n",
       "L 103.199426 133.078291 \n",
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       "L 103.254112 131.985628 \n",
       "L 103.3967 130.892965 \n",
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       "L 106.521178 122.151658 \n",
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       "L 107.138189 121.058995 \n",
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       "L 110.632798 115.595678 \n",
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       "L 117.990208 106.854372 \n",
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       "L 131.239627 96.003942 \n",
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       "L 135.726059 93.345195 \n",
       "L 136.847667 92.869827 \n",
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       "L 137.969275 92.440633 \n",
       "L 139.090883 92.025761 \n",
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       "L 142.669055 90.464422 \n",
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       "L 150.306963 88.462001 \n",
       "L 151.428571 88.326321 \n",
       "L 151.920555 88.279095 \n",
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       "L 161.523044 88.081123 \n",
       "L 162.219126 88.279095 \n",
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       "L 167.131084 90.002004 \n",
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       "L 168.252692 90.73657 \n",
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       "L 173.31044 97.020402 \n",
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       "L 174.239212 100.298392 \n",
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       "L 172.693554 114.503015 \n",
       "L 172.187429 115.595678 \n",
       "L 171.644607 116.688342 \n",
       "L 171.617516 116.74444 \n",
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       "L 170.589303 118.873668 \n",
       "L 170.495908 119.075473 \n",
       "L 170.078143 119.966332 \n",
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       "L 166.977912 125.429648 \n",
       "L 166.284054 126.522312 \n",
       "L 166.009476 126.94601 \n",
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       "L 149.185355 143.644197 \n",
       "L 148.676159 144.004925 \n",
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       "L 147.107689 145.097588 \n",
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       "L 92.712498 198.63809 \n",
       "z\n",
       "M 105.820183 175.692161 \n",
       "L 105.442642 175.643202 \n",
       "L 104.321034 175.512271 \n",
       "L 103.199426 175.371283 \n",
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       "L 76.969316 88.279095 \n",
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       "L 61.699928 101.62351 \n",
       "L 61.520126 101.391055 \n",
       "L 61.699928 100.435766 \n",
       "L 61.712675 100.298392 \n",
       "L 61.699928 100.035002 \n",
       "L 61.611679 99.205729 \n",
       "L 61.330383 98.113065 \n",
       "L 61.470141 97.020402 \n",
       "L 61.53134 95.927739 \n",
       "L 60.57832 95.34663 \n",
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       "L 59.308818 95.927739 \n",
       "L 58.611078 97.020402 \n",
       "L 58.498062 98.113065 \n",
       "L 58.710157 99.205729 \n",
       "L 58.54704 100.298392 \n",
       "L 58.383361 101.391055 \n",
       "L 58.935518 102.483719 \n",
       "L 59.154626 103.576382 \n",
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       "L 54.801111 113.410352 \n",
       "L 54.653623 114.503015 \n",
       "L 54.512643 115.595678 \n",
       "L 54.157502 116.688342 \n",
       "L 53.848672 117.063115 \n",
       "L 53.213207 117.781005 \n",
       "L 52.727064 118.311927 \n",
       "L 51.773154 118.873668 \n",
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       "L 50.483848 118.42319 \n",
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       "L 43.452753 142.912261 \n",
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       "L 38.572932 148.375578 \n",
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       "L 38.793187 153.838894 \n",
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       "L 34.781335 162.488709 \n",
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       "L 32.200801 165.858191 \n",
       "L 31.655709 166.950854 \n",
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       "L 31.142016 168.043518 \n",
       "L 30.662867 169.136181 \n",
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       "L 32.538119 171.057656 \n",
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       "L 33.659727 181.145784 \n",
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       "L 33.657103 182.248141 \n",
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       "L 34.81876 182.248141 \n",
       "L 35.902943 181.729148 \n",
       "L 37.024551 181.200488 \n",
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       "L 38.146159 180.660506 \n",
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       "L 40.331254 182.248141 \n",
       "L 40.159605 183.340804 \n",
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       "L 38.642664 198.63809 \n",
       "L 38.235444 199.730754 \n",
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       "L 39.267767 202.097113 \n",
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       "L 69.89696 217.213367 \n",
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       "L 66.18636 220.312773 \n",
       "L 66.011911 220.491357 \n",
       "L 65.583316 221.58402 \n",
       "z\n",
       "M 92.712498 198.63809 \n",
       "L 91.983345 198.372207 \n",
       "L 90.861737 197.980716 \n",
       "L 89.993236 197.545427 \n",
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       "L 86.375305 194.933349 \n",
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       "L 83.010481 194.34282 \n",
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       "L 81.888873 194.246127 \n",
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       "L 77.402441 193.330353 \n",
       "L 77.016119 193.174774 \n",
       "L 76.280833 192.851783 \n",
       "L 75.159225 192.285339 \n",
       "L 74.822114 192.082111 \n",
       "L 74.037617 191.382069 \n",
       "L 73.641691 190.989447 \n",
       "L 72.916009 190.300215 \n",
       "L 72.467298 189.896784 \n",
       "L 71.794401 189.340878 \n",
       "L 71.100786 188.804121 \n",
       "L 70.672793 188.484479 \n",
       "L 69.551185 187.972217 \n",
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       "L 68.429576 187.688318 \n",
       "L 67.307968 187.034508 \n",
       "L 66.937125 186.618794 \n",
       "L 66.311405 185.526131 \n",
       "L 66.18636 185.262724 \n",
       "L 65.919994 184.433467 \n",
       "L 65.835766 183.340804 \n",
       "L 65.860481 182.248141 \n",
       "L 65.719256 181.155477 \n",
       "L 65.064752 180.066288 \n",
       "L 65.060072 180.062814 \n",
       "L 63.943144 179.498338 \n",
       "L 62.821536 179.25155 \n",
       "L 61.94791 178.970151 \n",
       "L 61.699928 178.776856 \n",
       "L 61.212536 177.877487 \n",
       "L 60.968445 176.784824 \n",
       "L 60.771989 175.692161 \n",
       "L 60.63483 174.599497 \n",
       "L 60.57832 173.9792 \n",
       "L 60.537597 173.506834 \n",
       "L 60.347539 172.414171 \n",
       "L 59.988876 171.321508 \n",
       "L 59.544161 170.228844 \n",
       "L 59.456712 169.998551 \n",
       "L 59.121669 169.136181 \n",
       "L 58.787854 168.043518 \n",
       "L 58.497204 166.950854 \n",
       "L 58.335104 166.431449 \n",
       "L 58.105231 165.858191 \n",
       "L 57.495274 164.765528 \n",
       "L 57.213496 164.402304 \n",
       "L 56.474863 163.672864 \n",
       "L 56.091888 163.244192 \n",
       "L 55.69696 162.580201 \n",
       "L 55.649849 161.487538 \n",
       "L 56.01809 160.394874 \n",
       "L 56.091888 160.272252 \n",
       "L 56.69727 159.302211 \n",
       "L 57.213496 158.529463 \n",
       "L 57.419953 158.209548 \n",
       "L 58.062829 157.116884 \n",
       "L 58.335104 156.39232 \n",
       "L 58.479961 156.024221 \n",
       "L 58.573454 154.931558 \n",
       "L 58.335104 153.939979 \n",
       "L 58.306412 153.838894 \n",
       "L 57.929042 152.746231 \n",
       "L 57.769832 151.653568 \n",
       "L 57.803647 150.560905 \n",
       "L 57.841557 149.468241 \n",
       "L 57.828509 148.375578 \n",
       "L 57.844895 147.282915 \n",
       "L 57.948428 146.190251 \n",
       "L 58.091418 145.097588 \n",
       "L 58.183728 144.004925 \n",
       "L 58.215563 142.912261 \n",
       "L 58.335104 141.930851 \n",
       "L 58.349291 141.819598 \n",
       "L 58.730856 140.726935 \n",
       "L 59.260273 139.634271 \n",
       "L 59.456712 139.176451 \n",
       "L 59.74826 138.541608 \n",
       "L 60.051651 137.448945 \n",
       "L 60.239399 136.356281 \n",
       "L 60.474526 135.263618 \n",
       "L 60.57832 134.931664 \n",
       "L 60.844309 134.170955 \n",
       "L 61.230289 133.078291 \n",
       "L 61.560862 131.985628 \n",
       "L 61.699928 131.465358 \n",
       "L 61.868671 130.892965 \n",
       "L 62.169555 129.800302 \n",
       "L 62.560331 128.707638 \n",
       "L 62.821536 128.241537 \n",
       "L 63.18563 127.614975 \n",
       "L 63.943144 126.64618 \n",
       "L 64.046363 126.522312 \n",
       "L 65.064752 125.49473 \n",
       "L 65.134291 125.429648 \n",
       "L 66.18636 124.48237 \n",
       "L 66.350207 124.336985 \n",
       "L 67.307968 123.400304 \n",
       "L 67.45297 123.244322 \n",
       "L 68.300979 122.151658 \n",
       "L 68.429576 121.973459 \n",
       "L 68.981598 121.058995 \n",
       "L 69.551185 120.020352 \n",
       "L 69.579124 119.966332 \n",
       "L 70.052559 118.873668 \n",
       "L 70.371603 117.781005 \n",
       "L 70.612698 116.688342 \n",
       "L 70.672793 116.478159 \n",
       "L 70.950403 115.595678 \n",
       "L 71.44786 114.503015 \n",
       "L 71.794401 113.907812 \n",
       "L 72.104607 113.410352 \n",
       "L 72.819934 112.317688 \n",
       "L 72.916009 112.172192 \n",
       "L 73.541904 111.225025 \n",
       "L 74.037617 110.48435 \n",
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       "L 75.079009 109.039698 \n",
       "L 75.159225 108.938099 \n",
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       "L 76.280833 107.695167 \n",
       "L 77.222929 106.854372 \n",
       "L 77.402441 106.709627 \n",
       "L 78.524049 105.85155 \n",
       "L 78.642966 105.761709 \n",
       "L 79.645657 104.955272 \n",
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       "L 80.767265 103.743973 \n",
       "L 80.895419 103.576382 \n",
       "L 81.518707 102.483719 \n",
       "L 81.888873 101.487918 \n",
       "L 81.928528 101.391055 \n",
       "L 82.067052 100.298392 \n",
       "L 81.888873 99.316918 \n",
       "L 81.861025 99.205729 \n",
       "L 81.708621 98.113065 \n",
       "L 81.888873 97.500673 \n",
       "L 82.019992 97.020402 \n",
       "L 82.648538 95.927739 \n",
       "L 83.010481 95.452232 \n",
       "L 83.535518 94.835075 \n",
       "L 84.132089 94.257069 \n",
       "L 84.815954 93.742412 \n",
       "L 85.253697 93.440082 \n",
       "L 86.375305 92.900287 \n",
       "L 87.029902 92.649749 \n",
       "L 87.496913 92.450272 \n",
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    "flavio.plots.density_contour(x, y, n_sigma=(1,2,3,4), col=1)"
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    "For low statistics - taking 500 points here for example - the `covariance_factor` can be used to tweak the smoothing kernel bandwidth"
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   "execution_count": 8,
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    "plt.figure(figsize=(4,4))\n",
    "plt.scatter(x[:500], y[:500], label='scatter plot', rasterized=True, s=0.2, c='k', alpha=0.5)\n",
    "\n",
    "flavio.plots.density_contour(x[:500], y[:500], filled=False, col=0, label='autom. cov. factor')\n",
    "flavio.plots.density_contour(x[:500], y[:500], filled=False, col=1, covariance_factor=0.2, label='cov. factor 0.2')\n",
    "flavio.plots.density_contour(x[:500], y[:500], filled=False, col=2, covariance_factor=0.6, label='cov. factor 0.6')\n",
    "\n",
    "plt.xlim([-5,5])\n",
    "plt.ylim([-5,5])\n",
    "plt.legend()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Joint 2D and 1D probability plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `density_contour_joint` allows to combined the 1D and 2D plot functions. See the [API docs](https://flav-io.github.io/apidoc/flavio/plots/plotfunctions.m.html#flavio.plots.plotfunctions.density_contour_joint) for details on the options."
   ]
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   "execution_count": 9,
   "metadata": {
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    "flavio.plots.density_contour_joint(x, y);"
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    "It is also simple to combine several distributions in a single joint plot. Just feed the output of the first call\n",
    "as keyword arguments to the second call:"
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       "L 95.450347 201.926862 \n",
       "L 95.709003 201.964306 \n",
       "z\n",
       "M 102.051861 185.250632 \n",
       "L 101.597724 185.063782 \n",
       "L 100.829302 184.712 \n",
       "L 100.225187 184.414948 \n",
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       "L 94.086199 177.729478 \n",
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       "L 93.597677 171.879692 \n",
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       "L 93.861394 170.208324 \n",
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       "L 93.950969 168.536957 \n",
       "L 94.048657 167.701273 \n",
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       "L 94.681925 165.20238 \n",
       "L 94.68431 165.194222 \n",
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       "L 95.209248 163.522855 \n",
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       "L 96.18926 161.015803 \n",
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       "L 98.022663 157.673068 \n",
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       "L 99.006162 156.001701 \n",
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       "L 100.069961 154.330333 \n",
       "L 100.671207 153.49465 \n",
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       "L 101.298185 152.658966 \n",
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       "L 102.366146 151.28884 \n",
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       "L 103.90299 149.474088 \n",
       "L 104.046779 149.316231 \n",
       "L 104.671412 148.643307 \n",
       "L 104.828857 148.480547 \n",
       "L 105.439834 147.864311 \n",
       "L 105.66214 147.644864 \n",
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       "L 106.533394 146.80918 \n",
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       "L 107.745101 145.66788 \n",
       "L 108.317374 145.137812 \n",
       "L 108.513523 144.956554 \n",
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       "L 110.169564 143.466445 \n",
       "L 110.818789 142.895156 \n",
       "L 111.124022 142.630761 \n",
       "L 111.587211 142.241342 \n",
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       "L 112.355633 141.617678 \n",
       "L 113.124056 141.017675 \n",
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       "L 114.6609 139.894764 \n",
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       "L 116.197744 138.984229 \n",
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       "L 117.734588 138.292408 \n",
       "L 118.50301 137.975108 \n",
       "L 119.271433 137.625584 \n",
       "L 119.28964 137.616659 \n",
       "L 120.039855 137.25139 \n",
       "L 120.808277 136.851461 \n",
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       "L 121.576699 136.476942 \n",
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       "L 126.187232 135.249496 \n",
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       "L 110.448466 181.159945 \n",
       "z\n",
       "M 114.888467 169.460372 \n",
       "L 114.57057 169.329578 \n",
       "L 114.032675 169.08333 \n",
       "L 113.609795 168.875394 \n",
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       "L 109.217842 157.7608 \n",
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       "L 110.784646 152.495993 \n",
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       "L 123.714794 137.711265 \n",
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       "L 127.480062 135.860903 \n",
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       "L 136.08639 134.092899 \n",
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       "L 142.096117 137.871527 \n",
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       "L 142.815125 139.041485 \n",
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       "L 143.337872 141.381399 \n",
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       "L 142.276556 148.986121 \n",
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       "L 142.00324 149.601133 \n",
       "L 141.759156 150.156078 \n",
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    "plt.figure(figsize=(4,4))\n",
    "axes = flavio.plots.density_contour_joint(x, y, col=0, label='Plot 1');\n",
    "flavio.plots.density_contour_joint(0.7*x+0.5, 0.7*y+0.5, col=1, label='Plot 2', **axes);\n",
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