Holmes, C. and Knorr-Held, Leonhard
Efficient simulation of Bayesian logistic regression models.
Collaborative Research Center 386, Discussion Paper 306
In this paper we highlight a data augmentation approach to inference in the Bayesian logistic regression model. We demonstrate that the resulting conditional likelihood of the regression coefficients is multivariate normal, equivalent to a standard Bayesian linear regression, which allows for efficient simulation using a block Gibbs sampler. We illustrate that the method is particularly suited to problems in covariate set uncertainty and random effects models.