Modelling binomial, Poisson and gamma observations spatially distributed over irregularly shaped domains

A novel method is introduced 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 numerical analysis techniques, and specifically makes use of the Finite Element Method, that provide a basis for piecewise polynomial
surfaces.

, Computational and Methodological Statistics (ERCIM 2013), Senate House, University of London, UK