Efficient Bayesian inference for COM-Poisson regression models

Chanialidis, C. , Evers, L. , Neocleous, T. and Nobile, A. (2017) Efficient Bayesian inference for COM-Poisson regression models. Statistics and Computing, 28(3), pp. 595-608. (doi: 0.1007/s11222-017-9750-x)

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Abstract

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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Chanialidis, Dr Charalampos and Nobile, Dr Agostino and Evers, Dr Ludger and Neocleous, Dr Tereza
Authors: Chanialidis, C., Evers, L., Neocleous, T., and Nobile, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Statistics and Computing
Publisher:Springer
ISSN:0960-3174
ISSN (Online):1573-1375
Published Online:24 April 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Statistics and Computing 28(3):595-608
Publisher Policy:Reproduced under a Creative Commons License

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