TY - JOUR

T1 - Efficient Bayesian inference for COM-Poisson regression models

AU - Chanialidis, Charalampos

AU - Evers, Ludger

AU - Neocleous, Tereza

AU - Nobile, Agostino

N1 - © The Author(s) 2017. This article is an open access publication

PY - 2018/5

Y1 - 2018/5

N2 - COM-Poisson regression is an increasingly popular model for count data. Its main advantage is that it permits to model separately the mean and the variance of the counts, thus allowing the same covariate to affect in different ways the average level and the variability of the response variable. A key limiting factor to the use of the COM-Poisson distribution is the calculation of the normalisation constant: its accurate evaluation can be time-consuming and is not always feasible. We circumvent this problem, in the context of estimating a Bayesian COM-Poisson regression, by resorting to the exchange algorithm, an MCMC method applicable to situations where the sampling model (likelihood) can only be computed up to a normalisation constant. The algorithm requires to draw from the sampling model, which in the case of the COM-Poisson distribution can be done efficiently using rejection sampling. We illustrate the method and the benefits of using a Bayesian COM-Poisson regression model, through a simulation and two real-world data sets with different levels of dispersion.

AB - COM-Poisson regression is an increasingly popular model for count data. Its main advantage is that it permits to model separately the mean and the variance of the counts, thus allowing the same covariate to affect in different ways the average level and the variability of the response variable. A key limiting factor to the use of the COM-Poisson distribution is the calculation of the normalisation constant: its accurate evaluation can be time-consuming and is not always feasible. We circumvent this problem, in the context of estimating a Bayesian COM-Poisson regression, by resorting to the exchange algorithm, an MCMC method applicable to situations where the sampling model (likelihood) can only be computed up to a normalisation constant. The algorithm requires to draw from the sampling model, which in the case of the COM-Poisson distribution can be done efficiently using rejection sampling. We illustrate the method and the benefits of using a Bayesian COM-Poisson regression model, through a simulation and two real-world data sets with different levels of dispersion.

U2 - 10.1007/s11222-017-9750-x

DO - 10.1007/s11222-017-9750-x

M3 - Article

VL - 28

SP - 595

EP - 608

JO - Statistics and computing

JF - Statistics and computing

SN - 0960-3174

IS - 3

ER -