(2012) Brinchmann-Halvorsen, Kjetil; Ayala-Bravo, Víctor; Universidad Católica del Norte
The goal of this thesis is to develop methods for spatial interpolation of a tensor field, that is, a spatially correlated field of positive definite matrices. We develop a Wishart model for the field, and prove results needed for estimation of parameters using composite likelihood methods. We use this methodology to compute an interpolation in one example. The first chapter gives a summary of prior work and of some ideas we need, specifically likelihood and composite likelihood. The second chapter develops the Wishart random field model. The third chapter develop some distribution theory for the Wishart distribution that we need for the composite likelihood function, and the fourth chapter discusses estimation and prediction. The final chapter concludes and gives some challenges for further work.
