{ "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": "2024-05-20T23:21:39.176093Z", "iopub.status.busy": "2024-05-20T23:21:39.175729Z", "iopub.status.idle": "2024-05-20T23:21:40.545437Z", "shell.execute_reply": "2024-05-20T23:21:40.544562Z" } }, "outputs": [], "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": "2024-05-20T23:21:40.549656Z", "iopub.status.busy": "2024-05-20T23:21:40.549174Z", "iopub.status.idle": "2024-05-20T23:21:42.688925Z", "shell.execute_reply": "2024-05-20T23:21:42.688136Z" } }, "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": "2024-05-20T23:21:42.698120Z", "iopub.status.busy": "2024-05-20T23:21:42.697528Z", "iopub.status.idle": "2024-05-20T23:21:42.704294Z", "shell.execute_reply": "2024-05-20T23:21:42.703614Z" } }, "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": "2024-05-20T23:21:42.706967Z", "iopub.status.busy": "2024-05-20T23:21:42.706604Z", "iopub.status.idle": "2024-05-20T23:21:42.840702Z", "shell.execute_reply": "2024-05-20T23:21:42.839930Z" } }, "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 }