Bayesian analysis of the multinomial probit model

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 identi—ed parameter space. The key is the speci—cation of a prior on the covariance matrix so that the (1,1) element if —xed 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. Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, Illinois 60637. email: peter.rossi@gsb.uchicago.edu.

[1]  R. Kass,et al.  Nonconjugate Bayesian Estimation of Covariance Matrices and its Use in Hierarchical Models , 1999 .

[2]  B. R. Dansie.  PARAMETER ESTIMABILITY IN THE MULTINOMIAL PROBIT MODEL , 1985 .

[3]  V. Hajivassiliou,et al.  Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models , 1993 .

[4]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[5]  D. McFadden,et al.  The method of simulated scores for the estimation of LDV models , 1998 .

[6]  Xiao-Li Meng,et al.  Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage , 2000 .

[7]  Aviv Nevo.  Measuring Market Power in the Ready-to-Eat Cereal Industry , 1998 .

[8]  Gary Koop,et al.  Bayesian analysis of logit models using natural conjugate priors , 1993 .

[9]  J. Berger,et al.  Estimation of a Covariance Matrix Using the Reference Prior , 1994 .

[10]  D. McFadden.  A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration , 1989 .

[11]  D. S. Bunch,et al.  Estimability in the Multinomial Probit Model , 1989 .

[12]  Agostino Nobile,et al.  A hybrid Markov chain for the Bayesian analysis of the multinomial probit model , 1998, Stat. Comput..

[13]  Siddhartha Chib,et al.  MCMC Methods for Fitting and Comparing Multinomial Response Models , 1998 .

[14]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[15]  Kai Li.  Essays in Bayesian financial econometrics , 1996 .

[16]  Peter E. Rossi,et al.  A Bayesian analysis of the multinomial probit model with fully identified parameters , 2000 .

[17]  Peter E. Rossi,et al.  Stochastic Volatility: Univariate and Multivariate Extensions , 1999 .

[18]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[19]  Dale J. Poirier,et al.  Learning about the across-regime correlation in switching regression models , 1997 .

[20]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[21]  Dale J. Poirier,et al.  REVISING BELIEFS IN NONIDENTIFIED MODELS , 1998, Econometric Theory.