{ "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": "2024-12-07T00:38:17.317772Z", "iopub.status.busy": "2024-12-07T00:38:17.317000Z", "iopub.status.idle": "2024-12-07T00:38:18.599472Z", "shell.execute_reply": "2024-12-07T00:38:18.598756Z" } }, "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": "2024-12-07T00:38:18.604130Z", "iopub.status.busy": "2024-12-07T00:38:18.603830Z", "iopub.status.idle": "2024-12-07T00:38:20.367456Z", "shell.execute_reply": "2024-12-07T00:38:20.366742Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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": "2024-12-07T00:38:20.374593Z", "iopub.status.busy": "2024-12-07T00:38:20.374180Z", "iopub.status.idle": "2024-12-07T00:38:20.381671Z", "shell.execute_reply": "2024-12-07T00:38:20.380981Z" } }, "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": "2024-12-07T00:38:20.384946Z", "iopub.status.busy": "2024-12-07T00:38:20.384753Z", "iopub.status.idle": "2024-12-07T00:38:20.493763Z", "shell.execute_reply": "2024-12-07T00:38:20.493143Z" } }, "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": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 4 }