  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.
