1. Markov property The Markov property of a stochastic sequence {Xn}n≥0 implies that for all n ≥ 1, Xn is independent of (Xk : k / ∈ {n− 1, n, n + 1}), given (Xn−1, Xn+1). Another way to write this is: Xn ⊥ (Xk : k / ∈ ∂{n}) | (Xk : k ∈ ∂{n}) where ∂{n} is the set of neighbors of site n. We would like to now generalize this Markov property from one-dimensional index sets to more arbitrary domains.

in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

This article presents a novel algorithm for image segbeen developed for classification purposes. In addition, many mentation via the use of the multiresolution wavelet analysis and the authors have discovered significant advantages in the use of the expectation maximization (EM) algorithm. The development of a multiresolution concept [4,5] . Brazkovic and Neskovic presented multiresolution wave...

The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed. In order such successfully, sophisticated optimization chain Monte Carlo methods usually required. this paper, our focus is largely on reviewing recently developed difference priors, while introducing ...

GAUSSIAN MARKOV RANDOM FIELD MODELS FOR SURVEILLANCE ERROR AND GEOGRAPHIC BOUNDARIES