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.