Rejoinder on: Some recent work on multivariate Gaussian Markov random fields

Approximating Hidden Gaussian Markov Random Fields

This paper discusses how to construct approximations to a unimodal hidden Gaussian Markov random field on a graph of dimensionnwhen the likelihood consists of mutually independent data. We demonstrate that a class of non-Gaussian approximations can be constructed for a wide range of likelihood models. They have the appealing properties that exact samples can be drawn from them, the normalisatio...

Subset Selection for Gaussian Markov Random Fields

Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, called Gaussian free fields, which arise in semi-supervised learning and computer ...

Gaussian Markov Random Fields: Theory and Applications

Some further clarification on Markov chain random fields and transiograms

The Markov chain random field (MCRF) theory and the transiogram spatial measure were proposed several years ago. Basic sequential simulation algorithms based on simple MCRF models such as the Markov chain sequential simulation algorithm and the Markov chain sequential co-simulation algorithm have been developed and used in a series of application studies. However, misunderstanding of these two ...

Maximum a posteriori estimation for Markov chains based on Gaussian Markov random fields

In this paper, we present a Gaussian Markov random field (GMRF) model for the transition matrices (TMs) of Markov chains (MCs) by assuming the existence of a neighborhood relationship between states, and develop the maximum a posteriori (MAP) estimators under different observation conditions. Unlike earlier work on TM estimation, our method can make full use of the similarity between different ...