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Activity Number: 57 - Developments in Bayesian Spatial and Spatio-Temporal Modeling of Small Area Health Data
Type: Topic Contributed
Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #329436 Presentation
Title: Spatio-Temporal Models for Big Multinomial Data Using the Conditional Multivariate Logit-Beta Distribution
Author(s): Scott H. Holan* and Jonathan R Bradley and Christopher K. Wikle
Companies: University of Missouri/U.S. Census Bureau and Florida State University and University of Missouri
Keywords: Bayesian hierarchical model; Big data; Polya-Gamma; Markov chain Monte Carlo; Generalized Linear Mixed Model; Gibbs sampler

We introduce a Bayesian approach for analyzing high-dimensional multinomial data that are referenced over space and time. In particular, we define a multinomial data model with logit link to a latent spatio-temporal mixed effects model. This strategy allows for complex dependencies including nonstationarity in both space and time, asymmetry, non-seprable covariances, and parsimony. We also introduce the use of the conditional multivariate logit-beta distribution into the dependent multinomial data setting, which leads to conjugate full-conditional distributions for use in a Gibbs sampler. We refer to this model as the multinomial spatio-temporal mixed effects model (MN-STM). Additionally, we provide methodological developments including: the derivation of the associated full-conditional distributions, relationships with the multivariate normal distribution, and the stability of the non-stationary vector autoregressive model. We illustrate the MN-STM through simulations and through a demonstration using data from the Longitudinal Employer Household Dynamics (LEHD) program of the U.S. Census Bureau.

Authors who are presenting talks have a * after their name.

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