Bayesian Analysis

Sequential Bayesian Analysis of Multivariate Count Data

Tevfik Aktekin, Nick Polson, and Refik Soyer

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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.

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Bayesian Anal. (2017), 25 pages.

First available in Project Euclid: 23 March 2017

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state space count time series multivariate poisson scaled beta prior particle learning

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Aktekin, Tevfik; Polson, Nick; Soyer, Refik. Sequential Bayesian Analysis of Multivariate Count Data. Bayesian Anal., advance publication, 23 March 2017. doi:10.1214/17-BA1054.

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