Bayesian Inference of Latent Gaussian Graphical Models for Mixed Data

• Activity Number: 297 - SBSS Student Travel Award Session 1
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Zehang Li* and Tyler McCormick and Samuel Clark
• Companies: University of Washington and University of Washington and The Ohio State University
• Keywords: Gaussian graphical model; Bayesian inference; Mixed data

Abstract

Learning the dependence relationships among large numbers of continuous and discrete variables from relatively few observations is a statistical challenge that appears in a variety of scientific fields. In this work we introduce a latent Gaussian graphical modeling approach to characterize the underlying dependence relationships between variables of mixed types. We propose a new spike-and-slab prior for sparse inverse correlation matrices, and an efficient Markov chain Monte Carlo algorithm to sample from the resulting posterior distribution. This approach allows us to incorporate informative priors on the marginal distribution of variables directly. We further extend the framework to mixtures of latent Gaussian models for semi-supervised classification tasks with marginal informative priors and insufficient or no training data. Our work is motivated by survey-based cause of death instruments, known as verbal autopsies (VAs).