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Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexiblemodeling approach of the relationship between predictors and count responsevariables. The applications of HBPRMs to large-scale datasets require efficientinference algorithms due to the high computational cost of inferring many modelparameters based on random sampling. Although Markov Chain Monte Carlo (MCMC)algorithms have been widely used for Bayesian inference, sampling using thisclass of algorithms is time-consuming for applications with large-scale dataand time-sensitive decision-making, partially due to the non-conjugacy of manymodels. To overcome this limitation, this research develops an approximateGibbs sampler (AGS) to efficiently learn the HBPRMs while maintaining theinference accuracy. In the proposed sampler, the data likelihood isapproximated with Gaussian distribution such that the conditional posterior ofthe coefficients has a closed-form solution. Numerical experiments using realand synthetic datasets with small and large counts demonstrate the superiorperformance of AGS in comparison to the state-of-the-art sampling algorithm,especially for large datasets.

Approximate Gibbs Sampler for Efficient Inference of Hierarchical Bayesian Models for Grouped Count Data