Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models

TL;DR

This paper introduces a Monte Carlo-based method to approximate the Cramer-Rao bound for Markov random field parameters, enabling performance assessment of estimators in models like Ising and Potts.

Contribution

It formulates the bound computation as a statistical inference problem solvable with high accuracy Monte Carlo methods, overcoming intractability issues.

Findings

Successfully applied to Ising and Potts models

Assessed performance of three state-of-the-art estimators

Provided a practical approach for intractable likelihoods

Abstract

This report considers the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models.% where it is used to assess the performance of three state-of-the art estimators of the parameter of these Markov random fields.