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Paper No. 08-13

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TCO Fonseca and MFJ Steel

A new class of nonseparable space-time covariance models

Abstract: The aim of this work is to construct nonseparable, stationary covariance functions for processes that vary continuously in space and time. Stochastic modeling of phenomena over space and time is important in many areas of applications such as environmental sciences, agriculture and meteorology. But choice of an appropriate model can be difficult as one must take care to use valid covariance structures. A common choice for the process is a product of purely spatial and temporal random processes. In this case, the resulting process possesses a separable covariance function. Although these models are guaranteed to be valid, they are severely limited, since they do not allow space-time interactions. In this work we propose a general and flexible way of constructing valid nonseparable covariance functions derived through mixing over separable covariance functions. The proposed model allows for different degrees of smoothness across space and time and long-range dependence in time. Moreover, our proposal has as particular cases several covariance models proposed in the literature such as the Matérn and the Cauchy Class. We use a Markov chain Monte Carlo sampler for Bayesian inference and apply our modeling approach to the Irish wind data.

Keywords: Bayesian Inference; Irish wind data; Mixtures; Spatiotemporal modelling.