Generalized models for spatial regression with differential penalization

We introduce a novel method for the analysis of spatially distributed data from an exponential family distribution, able to efficiently deal with data occurring over irregularly shaped domains. The proposed generalized additive framework can handle all distributions within the exponential family, including binomial, Poisson and gamma outcomes, hence leading to a very broad applicability of the model. Specifically, we maximize a penalized log-likelihood function where the roughness penalty term involves a suitable differential operator of the spatial field over the domain of interest. Space-varying covariate information can also be included in the model in a semi-parametric setting. The proposed model exploits advanced scientific computing techniques and specifically makes use of the Finite Element Method, that provide a basis for piecewise polynomial surfaces.