Bayesian auxiliary variable models for binary and multinomial regression. (English) Zbl 1331.62142

Holmes, Chris C.; Held, Leonhard

Bayesian Anal. 1, No. 1, 145-168 (2006).

Summary: In this paper we discuss auxiliary variable approaches to Bayesian binary and multinomial regression. These approaches are ideally suited to automated Markov chain Monte Carlo simulation. In the first part we describe a simple technique using joint updating that improves the performance of the conventional probit regression algorithm. In the second part we discuss auxiliary variable methods for inference in Bayesian logistic regression, including covariate set uncertainty. Finally, we show how the logistic method is easily extended to multinomial regression models. All of the algorithms are fully automatic with no user set parameters and no necessary Metropolis-Hastings accept/reject steps.

MSC:

62F15	Bayesian inference
62J02	General nonlinear regression

Keywords:

auxiliary variables; Bayesian binary and multinomial regression; Markov chain Monte Carlo; model averaging; scale mixture of normals; variable selection