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Abstract:
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Multivariate geostatistical processes are used to model the joint relationship between multiple processes observed continuously in space. In many cases, modeling these processes jointly may enhance estimation and prediction over estimating the processes marginally, however a major difficulty remains to estimate the parameters in multivariate spatial models. For Gaussian processes, a valid multivariate spatial process requires that the covariance be non-negative definite. The Bivariate Matern process of Gneiting et al (2010) has well known constraints which guarantee a valid process. However, these constraints are rarely enforced in estimation and prediction. Using simulation studies, we examine the statistical properties of parameter estimates and predictions for multivariate Matern processes under such constraints. We compare to estimation and prediction of a commonly used multivariate model: the linear model of coregionalization (LMC). We close with a discussion of applications and extensions of this work
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