Fields From Markov Chains

From Markov Chains to Gibbs Fields

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

spMC: Modelling Spatial Random Fields with Continuous Lag Markov Chains

Abstract Currently, a part of the R statistical software is developed in order to deal with spatial models. More specifically, some available packages allow the user to analyse categorical spatial random patterns. However, only the spMC package considers a viewpoint based on transition probabilities between locations. Through the use of this package it is possible to analyse the spatial variabi...

Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues

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A Different Construction of Gaussian Fields from Markov Chains: Dirichlet Covariances

We study a class of Gaussian random elds with negative correlations. These elds are easy to simulate. They are de ned in a natural way from a Markov chain that has the index space of the Gaussian eld as its state space. In parallel with Dynkin's investigation of Gaussian elds having covariance given by the Green's function of a Markov process, we develop connections between the occupation times...