Sequential Bayesian Analysis of Multivariate Count Data

TL;DR

This paper introduces a new dynamic multivariate Poisson model, MPSB, enabling fast online updates and capturing serial and cross-series dependence, with applications demonstrated on consumer demand data.

Contribution

The paper develops the MPSB model with analytic state propagation, a particle learning algorithm, and new predictive distributions for multivariate count data.

Findings

Effective online updating of multivariate counts

Model captures serial and cross-series dependence

Demonstrated on consumer demand data

Abstract

We develop a new class of dynamic multivariate Poisson count models that allow for fast online updating and we refer to these models as multivariate Poisson-scaled beta (MPSB). The MPSB model allows for serial dependence in the counts as well as dependence across multiple series with a random common environment. Other notable features include analytic forms for state propagation and predictive likelihood densities. Sequential updating occurs through the updating of the sufficient statistics for static model parameters, leading 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 the dynamic multivariate negative binomial (DMNB) distribution. To illustrate our methodology, we use various simulation studies and count data on weekly non-durable goods consumer demand.