{ "cells": [ { "cell_type": "markdown", "id": "766ddb65-2b9c-4c08-85db-96fdae472503", "metadata": {}, "source": [ "# 0. Introduction to alea: a simple Gaussian model\n", "Welcome to alea: a Python package designed for constructing, handling, and fitting statistical models, computing confidence intervals and conducting sensitivity studies. Developed by the [XENON collaboration](https://xenonexperiment.org/), our aim is to provide an intuitive and flexible framework for statistical analysis.\n", "\n", "In this tutorial, you'll get to know alea by starting with a basic yet fundamental model: the Gaussian.\n", "We'll walk through model setup, data generation, and model fitting using generated data. This hands-on example will help you grasp the core concepts of alea and set you on the path to harnessing its capabilities for your own analyses. Let's dive in!" ] }, { "cell_type": "code", "execution_count": 1, "id": "a44a6f92-9962-493e-99a7-d2537b14e77b", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats\n", "\n", "from alea import GaussianModel" ] }, { "cell_type": "code", "execution_count": 2, "id": "737bec55", "metadata": {}, "outputs": [], "source": [ "# Just some plotting settings\n", "import matplotlib as mpl\n", "\n", "mpl.rcParams[\"figure.dpi\"] = 200\n", "mpl.rcParams[\"figure.figsize\"] = [4, 3]\n", "mpl.rcParams[\"font.family\"] = \"serif\"\n", "mpl.rcParams[\"font.size\"] = 9" ] }, { "cell_type": "markdown", "id": "20feeec8", "metadata": {}, "source": [ "## 0.1 Define the model" ] }, { "cell_type": "markdown", "id": "fc348f62", "metadata": {}, "source": [ "The simplest way to get started to just initialize a default `GaussianModel` without specifying anything else:" ] }, { "cell_type": "code", "execution_count": 3, "id": "a70f18b3", "metadata": {}, "outputs": [], "source": [ "model = GaussianModel()" ] }, { "cell_type": "markdown", "id": "ba3f4d2d", "metadata": {}, "source": [ "The instance `model` isn't of much use for now as we haven't specified anything. Let's have a look at the parameters of the model:" ] }, { "cell_type": "code", "execution_count": 4, "id": "11fa35da", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alea.parameters.Parameters(mu, sigma)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.parameters" ] }, { "cell_type": "markdown", "id": "460686fa", "metadata": {}, "source": [ "We can see that we have a parameter `mu`, which corresponds to the mean of the normal distribution, and a parameter `sigma`, which corresponds to its standard deviation. To learn more about the two parameters we can look at them individually:" ] }, { "cell_type": "code", "execution_count": 5, "id": "0423ec6b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alea.parameters.Parameter(name=mu, fittable=True)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.parameters.mu" ] }, { "cell_type": "code", "execution_count": 6, "id": "ec1603f4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alea.parameters.Parameter(name=sigma, fittable=True)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.parameters.sigma" ] }, { "cell_type": "markdown", "id": "d667f1cf", "metadata": {}, "source": [ "As we can see, right now, the only defined properties of both parameters are their names and whether they are fittable. Let's give the parameters nominal values and see what happens:" ] }, { "cell_type": "code", "execution_count": 7, "id": "f314d942", "metadata": {}, "outputs": [], "source": [ "model.parameters.mu.nominal_value = 1.0\n", "model.parameters.sigma.nominal_value = 0.1" ] }, { "cell_type": "code", "execution_count": 8, "id": "94ab7b23", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alea.parameters.Parameter(name=mu, nominal_value=1.0, fittable=True)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.parameters.mu" ] }, { "cell_type": "code", "execution_count": 9, "id": "f030acb8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alea.parameters.Parameter(name=sigma, nominal_value=0.1, fittable=True)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.parameters.sigma" ] }, { "cell_type": "markdown", "id": "31d6f441", "metadata": {}, "source": [ "## 0.2 Generate data from the model" ] }, { "cell_type": "markdown", "id": "5073acfc", "metadata": {}, "source": [ "This information is enough for the model to generate some data. Let's see what we can do:" ] }, { "cell_type": "code", "execution_count": 10, "id": "817f4534", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[array([(0.92670663,)], dtype=[('hat_mu', '" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Run the toy experiments\n", "datas = []\n", "for i in range(1000):\n", " data = model.generate_data()\n", " datas.append(data[0][\"hat_mu\"][0])\n", "\n", "\n", "# Visualize the distribution of the data and compare it to the nominal model\n", "plt.hist(datas, bins=50, density=True, label=\"generated\\ndata\")\n", "x = np.linspace(0.2, 1.8, 1000)\n", "plt.plot(\n", " x,\n", " stats.norm.pdf(\n", " x, loc=model.parameters.mu.nominal_value, scale=model.parameters.sigma.nominal_value\n", " ),\n", " label=\"nominal\\nGaussian model\",\n", ")\n", "\n", "# Cosmetics\n", "plt.xlim(0, 1.8)\n", "plt.xlabel(r\"$\\hat{\\mu}$\")\n", "plt.ylabel(\"Density\")\n", "plt.legend(loc=\"upper left\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2bcbc3a4", "metadata": {}, "source": [ "We can also change parameters in the data generation without modifying their nominal values by simply specifying them in the `generate_data` method. For example, we could generate data distributed around a mean of 0 instead of the nominal value of 0:" ] }, { "cell_type": "code", "execution_count": 12, "id": "d1e29187", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Run the toy experiments\n", "datas = []\n", "for i in range(1000):\n", " data = model.generate_data(mu=0)\n", " datas.append(data[0][\"hat_mu\"][0])\n", "\n", "\n", "# Visualize the distribution of the data and compare it to the nominal model\n", "plt.hist(datas, bins=50, density=True, label=\"generated\\ndata\")\n", "x = np.linspace(0.2, 1.8, 1000)\n", "plt.plot(\n", " x,\n", " stats.norm.pdf(\n", " x, loc=model.parameters.mu.nominal_value, scale=model.parameters.sigma.nominal_value\n", " ),\n", " label=\"nominal\\nGaussian model\",\n", ")\n", "x = np.linspace(-0.8, 0.8, 1000)\n", "plt.plot(\n", " x,\n", " stats.norm.pdf(x, loc=0, scale=model.parameters.sigma.nominal_value),\n", " label=\"modified\\nGaussian model\",\n", ")\n", "\n", "# Cosmetics\n", "plt.xlabel(r\"$\\hat{\\mu}$\")\n", "plt.ylabel(\"Density\")\n", "plt.legend(loc=\"upper right\", fontsize=7)\n", "plt.xlim(-1, 3)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a43a6e70", "metadata": {}, "source": [ "You can verify that the nominal values are unchanged:" ] }, { "cell_type": "code", "execution_count": 13, "id": "24fcd159", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'mu': 1.0, 'sigma': 0.1}" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.parameters.nominal_values" ] }, { "cell_type": "markdown", "id": "65ca1636", "metadata": {}, "source": [ "## 0.3 Fit the model to data" ] }, { "cell_type": "markdown", "id": "e293b38e", "metadata": {}, "source": [ "Now that we know how to generate data from the model we can assign it to the model and then find the parameters that maximize the likelihood." ] }, { "cell_type": "code", "execution_count": 14, "id": "d2850b84", "metadata": {}, "outputs": [], "source": [ "# generate data from the nominal model\n", "data = model.generate_data()\n", "\n", "# Assign the data to the model\n", "model.data = data" ] }, { "cell_type": "markdown", "id": "e8594a09", "metadata": {}, "source": [ "Now we want to perform the fit but we're only interested in the `mu` parameter, so we fix `sigma`:" ] }, { "cell_type": "code", "execution_count": 15, "id": "b41d425c", "metadata": {}, "outputs": [], "source": [ "model.parameters.sigma.fittable = False" ] }, { "cell_type": "code", "execution_count": 16, "id": "c7e42a32", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'mu': 1.0832352893133046, 'sigma': 0.1}" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "best_fit, max_ll = model.fit()\n", "best_fit" ] }, { "cell_type": "markdown", "id": "64205848", "metadata": {}, "source": [ "Let's visualize the likelihood minimization. We can access the log-likelihood of the model at a given value `x` of `mu` via `model.ll(mu=x)`. " ] }, { "cell_type": "code", "execution_count": 17, "id": "9e0577a5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Log Likelihood Ratio')" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Evaluate the log-likelihood at different values x of mu\n", "x = np.linspace(0.5, 1.5, 1000)\n", "y = -model.ll(mu=x)\n", "# Compute log-likelihood ratio\n", "y -= min(y)\n", "mle = best_fit[\"mu\"]\n", "\n", "# Plot\n", "plt.plot(x, y)\n", "plt.axvline(mle, label=f\"MLE={mle:.2f}\", color=\"red\")\n", "plt.axvline(\n", " model.data[0][\"hat_mu\"][0],\n", " label=f\"$\\hat{{\\mu}}$: {model.data[0]['hat_mu'][0]:.2f}\",\n", " ls=\":\",\n", " color=\"k\",\n", ")\n", "\n", "# Cosmetics\n", "plt.axhline(0.5, c=\"k\")\n", "plt.ylim(0, 2)\n", "plt.legend()\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"Log Likelihood Ratio\")" ] }, { "cell_type": "markdown", "id": "30cd04f5", "metadata": {}, "source": [ "## 0.4 Alternative model configuration" ] }, { "cell_type": "markdown", "id": "43eae4c5", "metadata": {}, "source": [ "Above, we configured the model step by step. However, there is also the option to directly configure the model parameters in the initialization:" ] }, { "cell_type": "code", "execution_count": 18, "id": "c47b23e6-b250-40dc-bd4d-246bbb16f547", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[array([(-0.1788163,)], dtype=[('hat_mu', '