The Markov property for generalized gaussian random fields

Differential Representation and Markov Property of Generalized Random Fields

Using the geometric properties of Sobolev spaces of integer order and a duality condition, the covariance operators of a generalized random field and its dual can be factorized. Via this covariance factorization, a representation of the generalized random field is obtained as a stochastic equation driven by generalized white noise. This stochastic equation becomes a differential equation under ...

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 ...

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...

Gaussian Markov Random Fields: Theory and Applications

Generalized Gaussian Random Fields using hidden selections

We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy tails in the marginal distribution. We present a Metropolis-Hastings algorithm for efficient simulation of realizations from the random field, and a numerical al...