Economics at your fingertips  

Some recent work on multivariate Gaussian Markov random fields

Ying C. MacNab ()
Additional contact information
Ying C. MacNab: University of British Columbia

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 3, 497-541

Abstract: Abstract Some recent work on conditional formulation of multivariate Gaussian Markov random fields is presented. The focus is on model constructions by compatible conditionals and coregionalization. Special attention is given to multivariate generalizations of univariate models. Beginning with univariate model constructions, a survey of key approaches to formulating multivariate extensions is presented. Two challenges in the formulation and implementation of multivariate models are highlighted: (1) entanglement of spatial and non-spatial components, and (2) enforcement for positivity condition. Managing the two challenges by decomposition, separation, and constrained parameterization is discussed. Also highlighted is the challenge of flexible modeling of (conditional) cross-spatial dependencies and, in particular, asymmetric cross-spatial dependencies. Interpretation of asymmetric cross-spatial dependencies is also discussed. A coregionalization framework which connects and unifies the various lines of model development is presented. The framework enables a systematic development of a broad range of models via linear and spatially varying coregionalization, respectively, with extensions to locally adaptive models. Formulation of multivariate models over variable-specific lattices is discussed. Selected models are illustrated with examples of Bayesian multivariate and spatiotemporal disease mapping. Potential applications of coregionalization models in imaging analysis, covariance modeling, dimension reduction, and latent variable analysis are briefly mentioned.

Keywords: Asymmetric cross-spatial dependencies; Conditional autoregressive model; Decomposition; Disease mapping; Entanglement; Gaussian Markov random fields; Linear model of coregionalization; Locally adaptive; Positivity; Separation; Spatially varying coregionalization; 62F15; 62F30; 62H10; 62H11; 62M40 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/11749/PS2

Access Statistics for this article

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Alfonso Gordaliza and Ana F. Militino

More articles in TEST: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla ().

Page updated 2019-04-09
Handle: RePEc:spr:testjl:v:27:y:2018:i:3:d:10.1007_s11749-018-0605-3