Bayesian Analysis

Bayesian auxiliary variable models for binary and multinomial regression

Leonhard Held and Chris C. Holmes

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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.

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Bayesian Anal. Volume 1, Number 1 (2006), 145-168.

First available in Project Euclid: 22 June 2012

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Auxiliary variables Bayesian binary and multinomial regression Markov chain Monte Carlo Model averaging Scale mixture of normals Variable selection


Holmes, Chris C.; Held, Leonhard. Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Anal. 1 (2006), no. 1, 145--168. doi:10.1214/06-BA105.

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See also

  • Related item: Ralf van der Lans. Bayesian estimation of the multinomial logit model: a comment on Holmes and Held, "Bayesian auxiliary variable models for binary and multinomial regression" . Bayesian Anal., Vol. 6, Iss.2 (2011), 353-355.