Dynamic Multiscale Spatiotemporal Models for Poisson Data

• Activity Number: 310
• Type: Invited
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Marco A.R. Ferreira and Thais Fonseca*+
• Companies: Universidade Federal do Rio de Janeiro and University of Missouri
• Keywords: Bayesian Dynamic models ; Massive datasets ; MCMC ; Multiscale modeling ; Time series models for counts ; Areal data

Abstract

We propose a new class of dynamic multiscale model for Poisson spatiotemporal processes. Specifically, we use a multiscale spatial Poisson factorization to decompose the Poisson process at each time point into spatiotemporal multiscale coefficients. These spatiotemporal multiscale coefficients are connected through time with a novel Dirichlet evolution. Further, we propose a simulation-based full Bayesian posterior analysis. Because the multiscale coefficients are conditionally independent a posteriori, our full Bayesian posterior analysis is scalable, computationally efficient, and highly parallelizable. Moreover, the Dirichlet evolution of each spatiotemporal multiscale coefficient is parametrized by a discount factor that encodes the relevance of the temporal evolution of the spatiotemporal multiscale coefficient. The analysis of discount factors provides a powerful way to identify regions with distinctive spatiotemporal dynamics. Finally, we illustrate the usefulness of our methodology with two applications, mortality ratios in the state of Missouri, and tornado reports in the American Midwest.