Generalized Spatial Splines Regression with Differential Penalization

We propose a novel method for the analysis of spatially distributed data from an exponential family distribution, able to efficiently treat data occurring over irregularly shaped domains.
We consider a generalized linear framework and extend the work of Sangalli (2013) to likelihoods other than the gaussian.
In particular, we can handle all distributions within the exponential family, including binomial, Poisson and Gamma outcomes,
hence leading to a very broad applicability of the proposed models. 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.
This maximization is done via a penalized iterative least square approach; see Wood (2006). Space-varying covariate information can also be included in the model in a semi-parametric setting. The proposed models exploit advanced scientific computing techniques and specifically make use of the Finite Element Method, that provide a basis for piecewise polynomial surfaces and allows to impose boundary conditions on the space distribution of the probability.

referente: laura.sangalli@polimi.it