A Gibbs sampling approach to Bayesian analysis of generalized linear models for binary data

A Monte Carlo Gibbs sampling approach is suggested for Bayesian posterior inference on unknown parameters in generalized linear models for binary data. This paper exploits the idea of Albert and Chib(1993), introducing normal latent variables into a model and connecting the binary response data with a normal linear model on continuous latent response data. Then all the full conditional distributions of unknown parameters are given by normal distributions with restrictions. Simple and accurate approximations to the restrictions are suggested so that the Gibbs sampler can be very easily implemented.