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June 2018 Sequential Bayesian Analysis of Multivariate Count Data
Tevfik Aktekin, Nick Polson, Refik Soyer
Bayesian Anal. 13(2): 385-409 (June 2018). DOI: 10.1214/17-BA1054

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.

Citation

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Tevfik Aktekin. Nick Polson. Refik Soyer. "Sequential Bayesian Analysis of Multivariate Count Data." Bayesian Anal. 13 (2) 385 - 409, June 2018. https://doi.org/10.1214/17-BA1054

Information

Published: June 2018
First available in Project Euclid: 23 March 2017

zbMATH: 06989953
MathSciNet: MR3780428
Digital Object Identifier: 10.1214/17-BA1054

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Vol.13 • No. 2 • June 2018
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