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The logistic regression model is the most popular model for analyzing binarydata. In the absence of any prior information, an improper flat prior is oftenused for the regression coefficients in Bayesian logistic regression models.The resulting intractable posterior density can be explored by running Polsonet al.'s (2013) data augmentation (DA) algorithm. In this paper, we establishthat the Markov chain underlying Polson et al.'s (2013) DA algorithm isgeometrically ergodic. Proving this theoretical result is practically importantas it ensures the existence of central limit theorems (CLTs) for sampleaverages under a finite second moment condition. The CLT in turn allows usersof the DA algorithm to calculate standard errors for posterior estimates.

Geometric ergodicity of Polya-Gamma Gibbs sampler for Bayesian logistic regression with a flat prior