Sequential Bayesian Analysis of Multivariate Count Data

• Activity Number: 319 - Highlights from Bayesian Analysis
• Type: Invited
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Tevfik Aktekin * and Nick Polson and Refik Soyer
• Companies: University of New Hampshire and University of Chicago and George Washington University
• Keywords: State Space ; Count Time Series ; Multivariate Poisson ; Scaled Beta Prior ; Particle Learning

Abstract

We develop a new class of dynamic multivariate Poisson count models that allow for fast online updating. We refer to this class as multivariate Poisson-scaled beta (MPSB) models. The MPSB model allows for serial dependence in count data as well as dependence with a random common environment across time series. Notable features of our model are analytic forms for state propagation, predictive likelihood densities, and sequential updating via sufficient statistics for the static model parameters. Our approach leads to a fully adapted particle learning algorithm and a new class of predictive likelihoods and marginal distributions which we refer to as the (dynamic) multivariate confluent hyper-geometric negative binomial distribution (MCHG-NB) and the dynamic multivariate negative binomial (DMNB) distribution, respectively. To illustrate our methodology, we use a simulation study and empirical data on weekly consumer non-durable goods demand.