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Paper No. 09-33

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TCO da Fonseca and MFJ Steel

Non-Gaussian Spatiotemporal Modelling through Scale Mixing

Abstract: The aim of this work is to construct non-Gaussian and nonseparable covariance functions for processes that vary continuously in space and time. Stochastic modelling of phenomena over space and time is important in many areas of application. But choice of an appropriate model can be difficult as one must take care to use valid covariance structures. We start from a general and flexible way of constructing valid nonseparable covariance functions derived through mixing over separable Gaussian covariance functions. We then generalize the resulting models by allowing for individual outliers as well as regions with larger variances. We induce this through scale mixing with separate positive-valued processes. Smooth mixing processes are applied to the underlying correlated Gaussian processes in space and in time, thus leading to regions in space and time of increased spread. We also apply a separate uncorrelated mixing process to the nugget effect to generate individual outliers. We consider posterior and predictive Bayesian inference with these models. We implement this through a Markov chain Monte Carlo sampler and apply our modelling approach to temperature data in the Basque country.

Keywords: Bayesian Inference; Flexible tails; Mixtures; Nonseparability; Outliers; Temperature data.