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Bayesian spatio‐temporal models based on discrete convolutions
Author(s) -
Sans Ó Bruno,
Schmidt Alexandra M.,
Nobre Aline A.
Publication year - 2008
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550360205
Subject(s) - kernel (algebra) , covariance , covariance function , mathematics , matérn covariance function , separable space , gaussian , isotropy , rational quadratic covariance function , gaussian process , statistical physics , computer science , combinatorics , statistics , covariance intersection , mathematical analysis , physics , quantum mechanics
The authors consider a class of models for spatio‐temporal processes based on convolving independent processes with a discrete kernel that is represented by a lower triangular matrix. They study two families of models. In the first one, spatial Gaussian processes with isotropic correlations are convoluted with a kernel that provides temporal dependencies. In the second family, AR(p) processes are convoluted with a kernel providing spatial interactions. The covariance structures associated with these two families are quite rich. Their covariance functions that are stationary and separable in space and time as well as time dependent nonseparable and nonisotropic ones.