Abstract
Given spatially located observed random variables (x, z = {(xi, zi)}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.
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