GENERALIZED PSEUDO-LIKELIHOOD ESTIMATES FOR MARKOV RANDOM FIELDS ON LATTICE

FUCHUN HUANG^{1} AND YOSIHIKO OGATA^{2}

1School of Computing and Mathematics, Deakin University, Victoria 3168, Australia,

e-mail: fuchun@deakin.edu.au

2The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan, e-mail: ogata@ism.ac.jp

(Received January 30, 1998; revised July 17, 2000)

Abstract. In this paper we generalize Besag’s pseudo-likelihood function for spatial statistical models on a region of a lattice. The correspondingly defined maximum generalized pseudo-likelihood estimates (MGPLEs) are natural extensions of Besag’s maximum pseudo-likelihood estimate (MPLE). The MGPLEs connect the MPLE and the maximum likelihood estimate. We carry out experimental calculations of the MG-PLEs for spatial processes on the lattice. These simulation results clearly show better performances of the MGPLEs than the MPLE, and the performances of differently defined MGPLEs are compared. These are also illustrated by the application to two real data sets.

Key words and phrases: Auto-normal model, Gibbs field, Ising model, pseudolikelihood.