Bayesian classication commonly relies on probit models, with data augmentation algorithms used for posterior computation. By imputing latent Gaussian variables, one can often trivially adapt computational approaches used in Gaussian models. However, MCMC for multinomial probit (MNP) models can be inecient in practice due to high posterior dependence between latent variables and parameters, and to diculties in eciently sampling latent variables when there are more than two categories. To address these problems, we propose a new class of diagonal orthant (DO) multinomial models. The key characteristics of these models include conditional independence of the latent variables given model parameters, avoidance of arbitrary identiability restrictions, and simple expressions for category probabilities. We show substantially improved computational eciency and comparable predictive performance to MNP.
['James E. Johndrow', 'David B. Dunson', 'Kristian Lum']
Diagonal Orthant Multinomial Probit Models