{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Prior Distributions with `Bilby`\n", "\n", "Prior distributions are a core component of any Bayesian problem and specifying them in codes can be one of the most confusing elements of a code.\n", "The `prior` modules in `Bilby` provide functionality for specifying prior distributions in a natural way.\n", "\n", "We have a range of predefined types of prior distribution and each kind has methods to:\n", "\n", "1. draw samples, `prior.sample`.\n", "2. calculate the prior probability, `prior.prob`.\n", "3. rescale samples from a unit cube to the prior distribution, `prior.rescale`.\n", " This is especially useful when using nested samplers as it avoids the need for rejection sampling.\n", "4. Calculate the log prior probability, `prior.log_prob`.\n", "\n", "In addition to the predefined prior distributions there is functionality to specify your own prior, either from a pair of arrays, or from a file.\n", "\n", "Each prior distribution can also be given a `name` and may have a different `latex_label` for plotting.\n", "If no name is provided, the default is `None` (this should probably by `''`)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-05T04:51:13.877944Z", "iopub.status.busy": "2024-04-05T04:51:13.877284Z", "iopub.status.idle": "2024-04-05T04:51:15.284999Z", "shell.execute_reply": "2024-04-05T04:51:15.284125Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/conda/envs/python310/lib/python3.10/site-packages/pandas/core/computation/expressions.py:21: UserWarning: Pandas requires version '2.8.4' or newer of 'numexpr' (version '2.7.3' currently installed).\n", " from pandas.core.computation.check import NUMEXPR_INSTALLED\n" ] } ], "source": [ "import bilby\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prior Instantiation\n", "\n", "Below we demonstrate instantiating a range of prior distributions.\n", "\n", "Note that when a `latex_label` is not specified, the `name` is used." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-05T04:51:15.292712Z", "iopub.status.busy": "2024-04-05T04:51:15.292019Z", "iopub.status.idle": "2024-04-05T04:51:17.346860Z", "shell.execute_reply": "2024-04-05T04:51:17.345992Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "\n", "priors = [\n", " bilby.core.prior.Uniform(minimum=5, maximum=50),\n", " bilby.core.prior.LogUniform(minimum=5, maximum=50),\n", " bilby.core.prior.PowerLaw(name=\"name\", alpha=2, minimum=100, maximum=1000),\n", " bilby.gw.prior.UniformComovingVolume(\n", " name=\"luminosity_distance\", minimum=100, maximum=1000, latex_label=\"label\"\n", " ),\n", " bilby.gw.prior.AlignedSpin(),\n", " bilby.core.prior.Gaussian(name=\"name\", mu=0, sigma=1, latex_label=\"label\"),\n", " bilby.core.prior.TruncatedGaussian(\n", " name=\"name\", mu=1, sigma=0.4, minimum=-1, maximum=1, latex_label=\"label\"\n", " ),\n", " bilby.core.prior.Cosine(name=\"name\", latex_label=\"label\"),\n", " bilby.core.prior.Sine(name=\"name\", latex_label=\"label\"),\n", " bilby.core.prior.Interped(\n", " name=\"name\",\n", " xx=np.linspace(0, 10, 1000),\n", " yy=np.linspace(0, 10, 1000) ** 4,\n", " minimum=3,\n", " maximum=5,\n", " latex_label=\"label\",\n", " ),\n", "]\n", "\n", "for ii, prior in enumerate(priors):\n", " fig.add_subplot(2, 5, 1 + ii)\n", " plt.hist(prior.sample(100000), bins=100, histtype=\"step\", density=True)\n", " if not isinstance(prior, bilby.core.prior.Gaussian):\n", " plt.plot(\n", " np.linspace(prior.minimum, prior.maximum, 1000),\n", " prior.prob(np.linspace(prior.minimum, prior.maximum, 1000)),\n", " )\n", " else:\n", " plt.plot(np.linspace(-5, 5, 1000), prior.prob(np.linspace(-5, 5, 1000)))\n", " plt.xlabel(\"{}\".format(prior.latex_label))\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define an Analytic Prior\n", "\n", "Adding a new analytic is achieved as follows." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-05T04:51:17.357357Z", "iopub.status.busy": "2024-04-05T04:51:17.356980Z", "iopub.status.idle": "2024-04-05T04:51:17.365651Z", "shell.execute_reply": "2024-04-05T04:51:17.364831Z" } }, "outputs": [], "source": [ "class Exponential(bilby.core.prior.Prior):\n", " \"\"\"Define a new prior class where p(x) ~ exp(alpha * x)\"\"\"\n", "\n", " def __init__(self, alpha, minimum, maximum, name=None, latex_label=None):\n", " super(Exponential, self).__init__(\n", " name=name, latex_label=latex_label, minimum=minimum, maximum=maximum\n", " )\n", " self.alpha = alpha\n", "\n", " def rescale(self, val):\n", " return (\n", " np.log(\n", " (np.exp(self.alpha * self.maximum) - np.exp(self.alpha * self.minimum))\n", " * val\n", " + np.exp(self.alpha * self.minimum)\n", " )\n", " / self.alpha\n", " )\n", "\n", " def prob(self, val):\n", " in_prior = (val >= self.minimum) & (val <= self.maximum)\n", " return (\n", " self.alpha\n", " * np.exp(self.alpha * val)\n", " / (np.exp(self.alpha * self.maximum) - np.exp(self.alpha * self.minimum))\n", " * in_prior\n", " )" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-05T04:51:17.369724Z", "iopub.status.busy": "2024-04-05T04:51:17.369311Z", "iopub.status.idle": "2024-04-05T04:51:17.499242Z", "shell.execute_reply": "2024-04-05T04:51:17.498484Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prior = Exponential(name=\"name\", alpha=-1, minimum=0, maximum=10)\n", "\n", "plt.figure(figsize=(12, 5))\n", "plt.hist(prior.sample(100000), bins=100, histtype=\"step\", density=True)\n", "plt.plot(\n", " np.linspace(prior.minimum, prior.maximum, 1000),\n", " prior.prob(np.linspace(prior.minimum, prior.maximum, 1000)),\n", ")\n", "plt.xlabel(\"{}\".format(prior.latex_label))\n", "plt.show()\n", "plt.close()" ] } ], "metadata": { "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.14" } }, "nbformat": 4, "nbformat_minor": 4 }