Efficient Posterior Sampling for Bayesian Poisson Regression

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In Bayesian context, however, there no sufficient specific computational tools efficient sampling from posterior distribution parameters, standard algorithms, such as random walk Metropolis-Hastings or Hamiltonian Monte Carlo typically used. Herein, we developed an algorithm importance sampler to simulate parameters under conditional Gaussian priors with superior performance respect state-of-the-art alternatives. The key both algorithms is introduction a proposal density based on approximation parameters. Specifically, our result leverages negative binomial likelihood successful P\'olya-gamma data augmentation scheme. Via simulation, obtained that time per independent sample proposed samplers competitive using sampling, showing all scenarios considered.