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Abstract:
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In this study, we explored different models for count data through an objective Bayesian perspective. The Poisson distribution is a standard distribution for count data analysis. To handle potential over- or under-dispersion as well as excess zeros in the data, we also considered negative Binomial, generalized Poisson, zero-inflated Poisson, zero-inflated negative Binomial and zero-inflated generalized Poisson distributions. These are distributions with one or two parameters, which need to impose a prior in the Bayesian analysis. The choice of priors is an important consideration in the objective Bayesian analysis. The objective priors we studied here include the uniform prior, the Jeffreys prior, and the reference prior. We examine the posterior propriety and compared the performance of these priors by checking credible interval coverage and the model selection results. The model selection among different count distributions was based on the fractional Bayesian factor and the logarithm of pseudo marginal likelihood. We carried out a large scale simulation study to show the importance of the appropriate choice of count models under different sample sizes.
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