  This is a technical report which explores the estimation methodologies on
hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random
Field. In first section, we briefly investigate a theoretical framework on
Metropolis-Hastings algorithm. Next, by using MH algorithm, we simulate the
data from Ising model, and study on how hyper-parameter estimation in Ising
model is enabled through MCMC algorithm using pseudo-likelihood approximation.
Following section deals with an issue on parameters estimation process of
Gaussian Hidden Markov Random Field using MAP estimation and EM algorithm, and
also discusses problems, found through several experiments. In following
section, we expand this idea on estimating parameters in Gaussian Hidden Markov
Spatial-Temporal Random Field, and display results on two performed
experiments.
