Griddy-Gibbs sampling for Bayesian P-splines models with Poisson data

Abstract: P-splines are appealing for smoothing Poisson distributed counts. They provide a flexible setting for modeling nonlinear model components based on a discretized penalty structure with a relatively simple computational backbone. Under a Bayesian inferential process relying on Markov chain Monte Carlo, estimates of spline coefficients are typically obtained by means of Metropolis-type algorithms, which may suffer from convergence issues if the proposal distribution is not properly chosen. To avoid such a sensitive calibration choice, we extend the Griddy-Gibbs sampler to Bayesian P-splines models with a Poisson response variable. In this model class, conditional posterior distributions of spline components are shown to have attractive mathematical properties. Despite their non-conjugate nature, conditional posteriors of spline coefficients can be efficiently explored with a Gibbs sampling scheme by relying on grid-based approximations. The proposed Griddy-Gibbs sampler for Bayesian P-splines (GGSBPS) algorithm is an interesting calibration-free tool for density estimation and histogram smoothing that is made available in a compact and user-friendly routine. The performance of our approach is assessed in different simulation settings and the GGSBPS algorithm is illustrated on two real datasets.