A hybrid Markov chain for the Bayesian analysis of the multinomial probit model

Authors:
Agostino Nobile
Affiliations:
Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK
Venue:
Statistics and Computing
Year:
1998

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Abstract

Bayesian inference for the multinomial probit model, using the Gibbs sampler with data augmentation, has been recently considered by some authors. The present paper introduces a modification of the sampling technique, by defining a hybrid Markov chain in which, after each Gibbs sampling cycle, a Metropolis step is carried out along a direction of constant likelihood. Examples with simulated data sets motivate and illustrate the new technique. A proof of the ergodicity of the hybrid Markov chain is also given.