{ "cells": [ { "cell_type": "markdown", "id": "a641832b", "metadata": {}, "source": [ "(emcee_conversion)=\n", "# Converting emcee objects to InferenceData\n", "\n", "{class}`~arviz.InferenceData` is the central data format for ArviZ. `InferenceData` itself is just a container that maintains references to one or more {class}`xarray.Dataset`. \n", "\n", "Below are various ways to generate an `InferenceData` from emcee objects." ] }, { "cell_type": "markdown", "id": "279a434d", "metadata": {}, "source": [ "```{seealso}\n", "\n", "- Conversion from Python, numpy or pandas objects\n", "- {ref}`xarray_for_arviz` for an overview of `InferenceData` and its role within ArviZ. \n", "- {ref}`schema` describes the structure of `InferenceData` objects and the assumptions made by ArviZ to ease your exploratory analysis of Bayesian models.\n", "```" ] }, { "cell_type": "markdown", "id": "b702e7fd", "metadata": {}, "source": [ "We will start by importing the required packages and defining the model. The famous 8 school model." ] }, { "cell_type": "code", "execution_count": 1, "id": "87f7958f", "metadata": {}, "outputs": [], "source": [ "import arviz as az\n", "import numpy as np\n", "import emcee" ] }, { "cell_type": "code", "execution_count": 2, "id": "9bdd7bbc", "metadata": {}, "outputs": [], "source": [ "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "7e9a05da", "metadata": {}, "outputs": [], "source": [ "J = 8\n", "y_obs = np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0])\n", "sigma = np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0])" ] }, { "cell_type": "code", "execution_count": 4, "id": "1cd28960", "metadata": {}, "outputs": [], "source": [ "def log_prior_8school(theta):\n", " mu, tau, eta = theta[0], theta[1], theta[2:]\n", " # Half-cauchy prior, hwhm=25\n", " if tau < 0:\n", " return -np.inf\n", " prior_tau = -np.log(tau**2 + 25**2)\n", " prior_mu = -((mu / 10) ** 2) # normal prior, loc=0, scale=10\n", " prior_eta = -np.sum(eta**2) # normal prior, loc=0, scale=1\n", " return prior_mu + prior_tau + prior_eta\n", "\n", "\n", "def log_likelihood_8school(theta, y, s):\n", " mu, tau, eta = theta[0], theta[1], theta[2:]\n", " return -(((mu + tau * eta - y) / s) ** 2)\n", "\n", "\n", "def lnprob_8school(theta, y, s):\n", " prior = log_prior_8school(theta)\n", " like_vect = log_likelihood_8school(theta, y, s)\n", " like = np.sum(like_vect)\n", " return like + prior" ] }, { "cell_type": "code", "execution_count": 5, "id": "cac78e4f", "metadata": {}, "outputs": [], "source": [ "nwalkers = 40 # called chains in ArviZ\n", "ndim = J + 2\n", "draws = 1500\n", "pos = np.random.normal(size=(nwalkers, ndim))\n", "pos[:, 1] = np.absolute(pos[:, 1])\n", "sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob_8school, args=(y_obs, sigma))\n", "sampler.run_mcmc(pos, draws);" ] }, { "cell_type": "markdown", "id": "cf6af8a4", "metadata": {}, "source": [ "## Manually set variable names\n", "This first example will show how to convert manually setting the variable names only, leaving everything else to ArviZ defaults." ] }, { "cell_type": "code", "execution_count": 6, "id": "95f696a0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
<xarray.Dataset>\n", "Dimensions: (chain: 40, draw: 1500)\n", "Coordinates:\n", " * chain (chain) int64 0 1 2 3 4 5 6 7 8 9 ... 30 31 32 33 34 35 36 37 38 39\n", " * draw (draw) int64 0 1 2 3 4 5 6 7 ... 1493 1494 1495 1496 1497 1498 1499\n", "Data variables:\n", " mu (chain, draw) float64 0.6982 0.7962 0.8433 ... 5.763 5.763 5.029\n", " tau (chain, draw) float64 0.6679 0.7259 0.8075 ... 2.051 2.051 3.239\n", " eta0 (chain, draw) float64 0.08153 0.008519 0.007711 ... 0.4684 0.6057\n", " eta1 (chain, draw) float64 -0.5837 -0.6358 -0.828 ... 1.431 1.431 1.608\n", " eta2 (chain, draw) float64 0.104 -0.003427 0.08645 ... -1.056 -0.8344\n", " eta3 (chain, draw) float64 0.8693 1.196 1.423 ... -1.621 -1.621 -0.8859\n", " eta4 (chain, draw) float64 0.8211 1.27 1.324 ... -1.509 -1.509 -0.9923\n", " eta5 (chain, draw) float64 0.04491 0.2302 0.1735 ... -0.8137 -0.5359\n", " eta6 (chain, draw) float64 0.2983 0.1357 0.1385 ... -0.2085 0.0377\n", " eta7 (chain, draw) float64 -0.5895 -0.5165 -0.6091 ... 0.1594 -0.03057\n", "Attributes:\n", " created_at: 2021-08-30T18:14:53.861857\n", " arviz_version: 0.11.2\n", " inference_library: emcee\n", " inference_library_version: 3.1.1
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<xarray.Dataset>\n", "Dimensions: (arg_0_dim_0: 8, arg_1_dim_0: 8)\n", "Coordinates:\n", " * arg_0_dim_0 (arg_0_dim_0) int64 0 1 2 3 4 5 6 7\n", " * arg_1_dim_0 (arg_1_dim_0) int64 0 1 2 3 4 5 6 7\n", "Data variables:\n", " arg_0 (arg_0_dim_0) float64 28.0 8.0 -3.0 7.0 -1.0 1.0 18.0 12.0\n", " arg_1 (arg_1_dim_0) float64 15.0 10.0 16.0 11.0 9.0 11.0 10.0 18.0\n", "Attributes:\n", " created_at: 2021-08-30T18:14:53.853598\n", " arviz_version: 0.11.2\n", " inference_library: emcee\n", " inference_library_version: 3.1.1
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