A Hybrid Markov Chain for the Bayesian Analysis of the Multinomial Probit Model (1995)

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. Several candidate distributions for the Metropolis step are considered. Examples with two simulated and one real data sets motivate and illustrate the new technique. A proof of the ergodicity of the hybrid Markov chain is also given. 

Keywords:

Multinomial probit model, Gibbs sampling, Metropolis algorithm, Bayesian analysis.