A Bayesian analysis of the multinomial probit model using marginal data augmentation

We introduce a set of new Markov chain Monte Carlo algorithms for Bayesian analysis of the multinomial probit model. Our Bayesian representation of the model places a new, and possibly improper, prior distribution directly on the identifiable parameters and thus is relatively easy to interpret and use. Our algorithms, which are based on the method of marginal data augmentation, involve only draws from standard distributions and dominate other available Bayesian methods in that they are as quick to converge as the fastest methods but with a more attractive prior specification. C-code along with an R interface for our algorithms is publicly available.1