On coregionalized multivariate Gaussian Markov random fields: construction, parameterization, and Bayesian estimation and inference

Ying C. MacNab ()
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Ying C. MacNab: University of British Columbia

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 1, No 10, 263-293

Abstract: Abstract Gaussian Markov random fields (GMRF) and their multivariate extensions (MGMRFs) are powerful tools for modelling probabilistic interactions of directly related variables. As an important category of graphical models, the potentials of (M)GMRF application are far-reaching. In this article, we review a class of coregionalized MGMRFs that coordinates, integrates, and generalizes the key MGMRFs in the literature. Theoretical and analytic results, including simulation and case studies, yield important insights into the model class, its options of parameterization, and the nature of asymmetry modelled by an asymmetric matrix of spatial parameters and its adaptive extensions. We show that while the Markovian interpretation of latent conditionals may be the main appeal of MGMRFs for some applications, another attraction of this model class is its coregionalization models that harness multidimensional interactions, dependencies, correlations, and variabilities for analysis of covariance structure. The latter is further illustrated by presenting models for shared component analysis, principal component analysis, and dimension reduction. The model class and its wide-ranging options for generalization are discussed for their richness and broad applicability to spatial and image data analytics and beyond.

Keywords: Analysis of covariance structure; Asymmetry; Bayesian estimation and inference; Departure from symmetry; Disease mapping; Dimensionality reduction; Linear coregionalization; Multivariate Gaussian Markov random fields; Principal component analysis; Shared component analysis; Small area estimation; Spatial dependence matrix; 62F15; 62F30; 62H10; 62H11; 62M40; 62P10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-022-00832-z

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