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Latent Gaussian random field mixture models

Journal article
Authors David Bolin
J. Wallin
F. Lindgren
Published in Computational Statistics & Data Analysis
Volume 130
Pages 80-93
ISSN 0167-9473
Publication year 2019
Published at Department of Mathematical Sciences
Pages 80-93
Language en
Links dx.doi.org/10.1016/j.csda.2018.08.0...
Keywords Random field, Spatial statistics, Gaussian mixture, Stochastic gradient, Geostatistics, Gaussian, markov random-fields, brain mr-images, stochastic-approximation, maximum-likelihood, gradient algorithm, em algorithm, segmentation, matrix
Subject categories Probability Theory and Statistics

Abstract

For many problems in geostatistics, land cover classification, and brain imaging the classical Gaussian process models are unsuitable due to sudden, discontinuous, changes in the data. To handle data of this type, we introduce a new model class that combines discrete Markov random fields (MRFs) with Gaussian Markov random fields. The model is defined as a mixture of several, possibly multivariate, Gaussian Markov random fields. For each spatial location, the discrete MRF determines which of the Gaussian fields in the mixture that is observed. This allows for the desired discontinuous changes of the latent processes, and also gives a probabilistic representation of where the changes occur spatially. By combining stochastic gradient minimization with sparse matrix techniques we obtain computationally efficient methods for both likelihood-based parameter estimation and spatial interpolation. The model is compared to Gaussian models and standard MRF models using simulated data and in application to upscaling of soil permeability data. (C) 2018 Elsevier B.V. All rights reserved.

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