A Bayesian analysis of the multinomial probit model with fully identified parameters

We present a new prior and corresponding algorithm for Bayesian analysis of the multinomial probit model. Our new approach places a prior directly on the identified parameter space. The key is the specification of a prior on the covariance matrix so that the (1,1) element if fixed at 1 and it is possible to draw from the posterior using standard distributions. Analytical results are derived which can be used to aid in assessment of the prior.