Bayesian Inference for Logistic Models Using Polya-Gamma Latent Variables

• 成果类型: Article
• 署名作者: Polson, Nicholas G.; Scott, James G.; Windle, Jesse
• 署名单位: University of Chicago; University of Texas System; University of Texas Austin; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.829001
• 发表日期: 2013
• 页码: 1339-1349
• 关键词: mixtures; binary

摘要

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Polya-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 Polya-Gamma distribution, are implemented in the R package BayesLogit. Supplementary materials for this article are available online.