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2013 The Polya-Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic
Hee Min Choi, James P. Hobert
Electron. J. Statist. 7: 2054-2064 (2013). DOI: 10.1214/13-EJS837


One of the most widely used data augmentation algorithms is Albert and Chib’s (1993) algorithm for Bayesian probit regression. Polson, Scott, and Windle (2013) recently introduced an analogous algorithm for Bayesian logistic regression. The main difference between the two is that Albert and Chib’s (1993) truncated normals are replaced by so-called Polya-Gamma random variables. In this note, we establish that the Markov chain underlying Polson, Scott, and Windle’s (2013) algorithm is uniformly ergodic. This theoretical result has important practical benefits. In particular, it guarantees the existence of central limit theorems that can be used to make an informed decision about how long the simulation should be run.


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Hee Min Choi. James P. Hobert. "The Polya-Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic." Electron. J. Statist. 7 2054 - 2064, 2013.


Published: 2013
First available in Project Euclid: 20 August 2013

zbMATH: 1349.60123
MathSciNet: MR3091616
Digital Object Identifier: 10.1214/13-EJS837

Primary: 60J27
Secondary: 62F15

Keywords: Data augmentation algorithm , Markov chain , minorization condition , Monte Carlo , Polya-Gamma distribution

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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