Bayesian Conway-Maxwell-Poisson model with spike-and slab priors for dispersed count data with application to football scores

Nick Zhang; Riccardo Rastelli; Nial Friel

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arXiv · 2607.18009

Bayesian Conway-Maxwell-Poisson model with spike-and slab priors for dispersed count data with application to football scores

Nick Zhang·Riccardo Rastelli·Nial Friel

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Abstract

Statistical modeling for goals scored in football is typically achieved using the Poisson distribution and its variants. Here we propose a Bayesian framework for modeling under- and over-dispersion in count data by combining the Conway-Maxwell-Poisson (CMP) likelihood with a spikeand-slab (SAS) prior on unit-specific dispersion parameters. The proposed methodology generalizes Poisson-based count data models by treating equidispersion as an explicit baseline, and offering probabilistic quantification of departures from this regime, while simultaneously estimating their magnitude. Posterior inference is performed through a tailored Metropolis-within-Gibbs sampler that handles the doubly-intractable likelihood and provides efficient posterior exploration. The new method is examined using simulated data to confirm its ability to capture non-equidispersion, and applied to English Premier League (EPL) data. Dispersion is modeled at the team level and linked to goal-scoring behavior, and allows for thresholding mechanisms to distinguish teams based on their posterior probability of non-equidispersion. The results reveal heterogeneities in team-specific dispersion in the EPL, and demonstrate improvements in both model fit and predictive performance with respect to the standard Poisson model.

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BibTeX RIS

Nick Zhang, Riccardo Rastelli, Nial Friel. 2026-07-20. Bayesian Conway-Maxwell-Poisson model with spike-and slab priors for dispersed count data with application to football scores. https://arxiv.org/abs/2607.18009

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