An approximate method of evaluating the joint likelihood for first-order GMRFs

摘要

A highly accurate approximation is proposed for computing the joint likelihood for first-order Gauss-Markov random fields (GMRFs) defined on irregularly shaped lattices. The problem in computing the likelihood lies in evaluating the determinant of a very large matrix B. Its exact evaluation is limited to either very small irregular regions or a few regularly shaped regions. The approximation proposed here is based on an eigenanalysis of B.