  Many of the data, particularly in medicine and disease mapping are count.
Indeed, the under or overdispersion problem in count data distrusts the
performance of the classical Poisson model. For taking into account this
problem, in this paper, we introduce a new Bayesian structured additive
regression model, called gamma count, with enough flexibility in modeling
dispersion. Setting convenient prior distributions on the model parameters is a
momentous issue in Bayesian statistics that characterize the nature of our
uncertainty parameters. Relying on a recently proposed class of penalized
complexity priors, motivated from a general set of construction principles, we
derive the prior structure. The model can be formulated as a latent Gaussian
model, and consequently, we can carry out the fast computation by using the
integrated nested Laplace approximation method. We investigate the proposed
methodology simulation study. Different expropriate prior distribution are
examined to provide reasonable sensitivity analysis. To explain the
applicability of the proposed model, we analyzed two real-world data sets
related to the larynx mortality cancer in Germany and the handball champions
league.
