From 6bb4ebae1469e6e03ec724dcc1e5611155707b62 Mon Sep 17 00:00:00 2001 From: Andrew McCluskey Date: Tue, 19 May 2020 15:33:59 +0100 Subject: [PATCH] max likelihood tutorial done --- docs/source/max_likelihood.ipynb | 89 ++++++++------------------------ 1 file changed, 21 insertions(+), 68 deletions(-) diff --git a/docs/source/max_likelihood.ipynb b/docs/source/max_likelihood.ipynb index b966b6c..962ff9b 100644 --- a/docs/source/max_likelihood.ipynb +++ b/docs/source/max_likelihood.ipynb @@ -11,16 +11,12 @@ "\n", "In this tutorial we will see how `uravu` can be used to maximize the likelihood of a model for some dataset.\n", "\n", - "In `uravu`, the likelihood is calculated as follows, \n", + "In `uravu`, when the sample is normally distributed the likelihood is calculated as follows, \n", "\n", - "$$ \\ln L = -0.5 \\sum_{i=1}^n \\bigg[ \\frac{(y_i - m_i) ^2}{s_i^2} + \\ln(2 \\pi s_i^2) \\bigg], $$\n", + "$$ \\ln L = -0.5 \\sum_{i=1}^n \\bigg[ \\frac{(y_i - m_i) ^2}{\\delta y_i^2} + \\ln(2 \\pi \\delta y_i^2) \\bigg], $$\n", "\n", - "where, $y$ is the data ordinate, $m$ is the model ordinate, and $s$ is, \n", - "\n", - "$$ s_i^2 = \\delta y_i^2 + f^2 m_i^2 $$,\n", - "\n", - "where $\\delta y$ is the uncertainty in $y$ and $f$ is the fraction of unaccounted uncertainty (more about this can be found in the [Unaccounted uncertainty](./unaccounted_uncertainty.html) tutorial.)\n", - "`uravu` is able to maximize this function using the [scipy.optimize.minimize()](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html) function (we minimize the negative of the likelihood).\n", + "where, $y$ is the data ordinate, $m$ is the model ordinate, and $\\delta y_i$ is uncertainty in $y$.\n", + "`uravu` is able to maximize this function using the [`scipy.optimize.minimize()`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html) function (we minimize the negative of the likelihood).\n", "\n", "Before we maximise the likelihood, is it necessary to create some *synthetic* data to analyse. " ] @@ -32,7 +28,9 @@ "outputs": [], "source": [ "import numpy as np\n", - "import matplotlib.pyplot as plt" + "import matplotlib.pyplot as plt\n", + "from uravu import plotting\n", + "from uravu.relationship import Relationship" ] }, { @@ -63,7 +61,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -76,6 +74,7 @@ ], "source": [ "plt.errorbar(x, y, dy, marker='o', ls='')\n", + "plt.yscale('log')\n", "plt.show()" ] }, @@ -83,7 +82,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The data plotted above may be modelled with the following relationship, \n", + "The data plotted above (note the logarthimic $y$-axis) may be modelled with the following relationship, \n", "\n", "$$ y = a\\exp(bx), $$\n", "\n", @@ -127,45 +126,7 @@ "metadata": {}, "outputs": [], "source": [ - "from uravu.relationship import Relationship" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "modeller = Relationship(my_model, x, y, dy)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Function Name: my_model \n", - "Abscissa: [ 0.00e+00 5.26e-01 ... 9.47e+00 1.00e+01 ] \n", - "Ordinate: [ 4.65e+00 4.89e+00 ... 4.58e+02 6.28e+02 ] \n", - "Ordinate uncertainty: [ 9.30e-01 9.77e-01 ... 9.16e+01 1.26e+02 ]\n", - "Abscissa Name: x \n", - "Ordinate Name: y \n", - "Abscissa Unit: dimensionless \n", - "Ordinate Unit: dimensionless \n", - "Variables: [ 1.00e+00 1.00e+00 ] \n", - "Unaccounted uncertainty: False \n", - "MCMC performed: False \n", - "Nested sampling performed: False \n", - "\n" - ] - } - ], - "source": [ - "print(modeller)" + "modeller = Relationship(my_model, x, y, ordinate_error=dy)" ] }, { @@ -173,33 +134,33 @@ "metadata": {}, "source": [ "The `Relationship` object gives us access to a few powerful Bayesian modelling methods.\n", - "However, this tutorial is focused on maximising the likelihood, this is achieved with the `max_likelihood()` class method. " + "However, this tutorial is focused on maximising the likelihood, this is achieved with the `max_likelihood()` class method, where the keyword `'mini'` indicates the standard [`scipy.optimize.minimize()`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html) function should be used. " ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ - "modeller.max_likelihood()" + "modeller.max_likelihood('mini')" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[3.82070367 0.50131519]\n" + "[4.55082086 0.46090669]\n" ] } ], "source": [ - "print(modeller.variables)" + "print(modeller.variable_medians)" ] }, { @@ -214,21 +175,12 @@ }, { "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "from uravu import plotting" - ] - }, - { - "cell_type": "code", - "execution_count": 12, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -241,6 +193,7 @@ ], "source": [ "ax = plotting.plot_relationship(modeller)\n", + "plt.yscale('log')\n", "plt.show()" ] }, @@ -268,7 +221,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.7.6" } }, "nbformat": 4,