Gaussian Markov Models for Adaptive Smoothing

Abstract

In this thesis, we study Gaussian Markov random field representation of the non-homogenous integrated Wiener process, for the purpose of doing adaptive smoothing of temporal data. We demonstrate that these representations are consistent for irregular locations, and derive Bayesian inferential algorithms with computational cost of only O(n), using numerical algorithms for band-matrices. We outline a more general purpose with the aim of doing more general generic adaptive smoothing of temporal data.