Statistics and Data Science Seminar
Dr. Xiao Zhang
Michgian Tech University
Parameter-Expanded Data Augmentation in Probit Models
Abstract: Probit models have been prominent tools to analyze binary/ordinal data, but the computational complexity of maximum likelihood functions presents challenges in their usage. Furthermore, the model identification necessitates the covariance matrix of the latent multivariate normal variables to be a correlation matrix, which brings a rigorous task to develop efficient Markov chain Monte Carlo (MCMC) sampling methods. Data augmentation has been inevitable explored for both identifiable univariate and multivariate probit models. Particularly, it is well-known that parameter-expanded data augmentation (PX-DA) based on non-identifiable models accelerates the convergence and improves the mixing of MCMC components. However, comprehensive investigation has seldom been undertaken, and various algorithms due to incorrectly constructed non-identifiable models further bring obstacles to develop efficient MCMC sampling methods. We tackle this issue by constructing correct non-identifiable models and develop PX-DA algorithms to estimate both univariate and multivariate probit models. Our investigation exhibits that the proposed PX-DA algorithms advance the performance of MCMC sampling considerably and illustrates the essentials of using PX-DA, especially for data with large sample sizes.
Wednesday March 18, 2026 at 4:15 PM in Zoom