Latent Gaussian random field mixture models

David Bolin, Jonas Wallin and Finn Lindgren

Computational Statistics & Data Analysis, 2019, vol. 130, issue C, 80-93

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.

Keywords: Random field; Spatial statistics; Gaussian mixture; Stochastic gradient; Geostatistics; Gaussian process (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:130:y:2019:i:c:p:80-93

DOI: 10.1016/j.csda.2018.08.007

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