Department Seminar Series: Somak Dutta, Lattice based approximations of Matérn dependence and related matrix-free statistical computations
In recent years, one major focus of modeling spatial data has been to connect two contrasting approaches, namely, the Markov random field approach and the geostatistical approach. While Markov random fields allow fast statistical computations, they can only accommodate discrete spatial variation. In contrast, the geostatistical models accommodate continuum spatial variation but are faced with formidable computational burden. In this talk, I will discuss my PhD dissertational work on lattice based approximations to the continuum Matérn dependence structure that occupies a central role in geostatistical literature. I will show how these approximations allow us to obtain both scalable statistical computations and inferences that mimic the same based on the continuum Matérn dependence. In particular, I will focus on mixed linear models and use h-likelihood methods for estimation and prediction. I will also discuss sophisticated algorithms that provide fast matrix-free answers to various inferential problems such as computing likelihood ratio statistics and simultaneous exceedance regions.