A computational Bayesian approach to Poisson regression models-a simulation study

Poisson regression is a kind of regression analysis that describes count data using a generalized linear model. A frequentist method for these models is to apply reweighted least-squares iteratively to determine the maximum likelihood estimators (MLE). In this study, we compare the effectiveness of frequentist and Bayesian computational techniques for estimating the parameters of the Poisson regression models. The Bayesian estimation approach was carried out using Markov Chain Monte Carlo (MCMC) algorithms. Two algorithms were presented: Hamiltonian Monte Carlo (HMC) and Random Walk Metropolis (RWM). The median of the mean absolute deviation (MMAD) was evaluated as a measure of the performance of estimators. The simulation results indicate that although the maximum likelihood technique on occasions performs better than the other methods in terms of the median of mean absolute deviation (MMAD) and the standard deviation (SD). However, the performance of the RWM appeared to be very good compared to the HMC in terms of convergence in the drawings.