Premium
Penalized Pseudolikelihood Inference in Spatial Interaction Models with Covariates
Author(s) -
Divino Fabio,
Frigessi Arnoldo,
Green Peter J.
Publication year - 2000
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00200
Subject(s) - mathematics , markov random field , random field , estimator , covariate , spline (mechanical) , markov chain monte carlo , monte carlo method , bayesian inference , algorithm , bayesian probability , parametric statistics , statistics , artificial intelligence , image (mathematics) , computer science , engineering , structural engineering , image segmentation
Given spatially located observed random variables ( x , z = {( x i , z i )} i , we propose a new method for non‐parametric estimation of the potential functions of a Markov random field p ( x | z ), based on a roughness penalty approach. The new estimator maximizes the penalized log‐pseudolikelihood function and is a natural cubic spline. The calculations involved do not rely on Monte Carlo simulation. We suggest the use of B‐splines to stabilize the numerical procedure. An application in Bayesian image reconstruction is described.