Title: Geometric ergodicity of Polya-Gamma Gibbs sampler for Bayesian logistic regression with a flat prior
Authors: Xin Wang - Miami University (United States) [presenting]
Abstract: The logistic regression model is the most popular model for analyzing binary data. In the absence of any prior information, an improper flat prior is often used for the regression coefficients in Bayesian logistic regression models. The resulting intractable posterior density can be explored by running the data augmentation (DA) algorithm. We establish that the Markov chain underlying the DA algorithm is geometrically ergodic. Proving this theoretical result is practically important as it ensures the existence of central limit theorems (CLTs) for sample averages under a finite second moment condition. The CLT in turn allows users of the DA algorithm to calculate standard errors for posterior estimates.