A comparison of computational approaches for posterior inference in Bayesian Poisson regression

Poisson regression is a well-established tool to study the effect of a set of covariates on a count variable of interest. While in the frequentist paradigm estimation of the coefficients has long been studied and refined, in the Bayesian framework it is customary to use general strategies, not explicitly targeted for this problem. Moving from the analysis of a dataset on the bicycle traffic on the Brooklyn Bridge in New York, where the variable of interest is the number of bikes crossing the bridge, we investigate the computational challenges of posterior inference for the Poisson log-linear model. We compare the performances of the well-known random-walk Metropolis-Hastings algorithm with those of the recently introduced algorithm of 2 implemented in the R package “bpr”.