This is a past event.

Please join the Department of Mathematical Sciences in Fisher Hall 326 on Thursday, April 2 from 12:00 - 1:00 p.m. for our Graduate Student Seminar Series. 

Refreshments will be provided.

Contact the Math Department Graduate Program Assistant, Andi Schoch, via email (ajschoch@mtu.edu) or in person (Fisher Hall 318) with any questions. 

Presenting this week is Suwash Silwal.

Title: Parameter-Expanded Data Augmentation for Analyzing Multivariate/Multiperiod  Nominal Measures with Missing Values Using Multivariate Multinomial Probit Models

Abstract: Multivariate nominal outcomes frequently arise in panel and multiperiod studies, where responses are inherently correlated and often subject to missingness. The multivariate multinomial probit (MMNP) model provides a flexible framework for capturing such dependence structures; however, Bayesian estimation is computationally challenging due to covariance identification constraints and slow mixing of Markov Chain Monte Carlo (MCMC) algorithms, particularly in the presence of missing data. In this paper, we develop a parameter-expanded data augmentation (PX-DA) approach for Bayesian inference in MMNP models with missing nominal outcomes under ignorable missing-data mechanisms. The proposed method relaxes restrictive identification constraints, substantially improving MCMC convergence and mixing compared to existing PX-Gibbs and PX-Metropolis–Hastings algorithms. Extensive simulation studies under missing completely at random (MCAR) and missing at random (MAR) scenarios, as well as real data applications, demonstrate that the proposed methods significantly improve the convergence and mixing of MCMC components across a range of sample sizes and missingness levels, thus enhancing the practical usage of MMNP models for multivariate discrete nominal data with missing values.