Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models
Computation
2013-09-18 v3 Methodology
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.
Cite
@article{arxiv.1206.3985,
title = {Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models},
author = {Marcelo Pereyra and Nicolas Dobigeon and Hadj Batatia and Jean-Yves Tourneret},
journal= {arXiv preprint arXiv:1206.3985},
year = {2013}
}