Latent Gaussian random field mixture models
Journal article, 2019

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.

Spatial statistics

Random field

Gaussian process

Stochastic gradient

Gaussian mixture



David Bolin

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Jonas Wallin

Lund University

Finn Lindgren

University of Edinburgh

Computational Statistics and Data Analysis

0167-9473 (ISSN)

Vol. 130 80-93


Basic sciences

Subject Categories

Physical Geography

Probability Theory and Statistics

Control Engineering



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