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Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables
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Journal Article
Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables
2013
Overview
We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya–Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effect models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that (1) circumvent the need for analytic approximations, numerical integration, or Metropolis–Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Pólya–Gamma distribution, are implemented in the R package BayesLogit . Supplementary materials for this article are available online.
Publisher
Taylor & Francis Group,Taylor & Francis Group, LLC,Taylor & Francis Ltd
Subject
