A Symmetric Prior for Multinomial Probit Models

TL;DR

This paper introduces a symmetric prior for Bayesian multinomial probit models that eliminates dependence on the base category and enables efficient sampling of covariance matrices.

Contribution

It proposes a novel symmetric prior and identification strategy that improves Bayesian multinomial probit modeling.

Findings

Prior becomes symmetric with respect to outcome relabeling

Efficient Gibbs sampling algorithm developed

No need for Metropolis-Hastings updates

Abstract

Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification strategy, and associated prior distribution for the model parameters, that renders the prior symmetric with respect to relabeling the outcome categories. The new prior permits an efficient Gibbs algorithm that samples rank-deficient covariance matrices without resorting to Metropolis-Hastings updates.