Markov chain Monte Carlo Algorithms for the Bayesian Logistic Regression Model

ISBN: 978-981-08-8407-9

Authors: Dobrin Marchev

Abstract:

In this paper we consider the Bayesian logistic regression model with flat prior. More specifically, we use the normal mixture representation of the logistic distribution to derive a new Markov chain Monte Carlo method for exploring the posterior density of the regression coefficients. This new algorithm is further improved by adding an extra step in the sampling scheme, thus making it a special case of Hobert and Marchev (2008) Haar PX-DA algorithm, which is known to be more efficient than the standard approach. The two methods are compared on a real dataset, where we demonstrate empirically that the Haar algorithm’s Markov chain mixes much better.

Keywords: Bayesian Logistic Regression, Gibbs Sampler, Kolmogorov-Smirnov distribution, MCMC