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Holmes, C. and Knorr-Held, Leonhard (2003): Efficient simulation of Bayesian logistic regression models. Collaborative Research Center 386, Discussion Paper 306
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Abstract

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.