Non-Gaussian Spatiotemporal Modeling Through Scale Mixing

• Activity Number: 102
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Thais C. O. Fonseca*+ and Mark F. J. Steel
• Companies: Unirio and Warwick University
• Keywords: non-Gaussian processes ; outlier detection ; Bayesian inference ; Mixture models ; Nonseparable covariances

Abstract

We construct non-Gaussian processes that vary continuously in space and time with nonseparable covariance functions. Stochastic modelling of phenomena over space and time is important in many areas of application. We start from a general and flexible way of constructing valid nonseparable covariance functions through mixing over separable 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 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 and implement this through a Markov chain Monte Carlo sampler. Finally, this modelling approach is applied to temperature data in the Basque country.