Bayesian inference for logistic models using Polya-Gamma latent variables
This provides a more efficient and easier-to-use approach for Bayesian statisticians and practitioners working with logistic regression and related models, though it is incremental as it builds on existing data-augmentation frameworks.
The authors tackled the problem of fully Bayesian inference for models with binomial likelihoods by introducing a new data-augmentation strategy using Polya-Gamma latent variables, resulting in simple and computationally efficient methods that outperform existing strategies and circumvent the need for approximations or Metropolis-Hastings.
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-effects 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. In the technical supplement appended to the end of the paper, we provide further details regarding the generation of Polya-Gamma random variables; the empirical benchmarks reported in the main manuscript; and the extension of the basic data-augmentation framework to contingency tables and multinomial outcomes.