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A General Class of Nonseparable Space-time CovarianceModelsThais Cristina Oliveira da Fonseca ∗University of Warwick, United KingdomMark F. J. SteelUniversity of Warwick, United KingdomThe aim of this work is to construct nonseparable, stationary covariance functions for processesthat vary continuously in space and time. Stochastic modelling of phenomena over space and time isimportant in many areas of application. But choice of an appropriate model can be difficult as we needto ensure that we use valid covariance structures. A common choice for the process is a product ofpurely spatial and temporal random processes. In this case, the resulting process possesses a separablecovariance function. Although these models are guaranteed to be valid, they are severely limited, sincethey do not allow space-time interactions. We propose a general and flexible class of valid nonseparablecovariance functions based on the mixture of separable covariance functions. The proposed model allowsfor different degrees of smoothness across space and time and long-range dependence in time. Moreover,the proposed class has as particular cases several covariance models proposed in the literature such asthe Matérn and the Cauchy Class. The proposed model easily allows for extensions e.g. to include anugget effect and asymmetries as we illustrate in the modeling of the Irish wind data.∗ Apresentador/Speaker31
Exact Simulation and Bayesian Inference for Jump-DiffusionProcessesFlávio B. Gonçalves ∗University of WarwickGareth O. RobertsUniversity of WarwickThe last 10 years have seen a large increase in statistical methodology for diffusions, and computationallyintensive Bayesian methods using data augmentation have been particulary prominent. This activityhas been fuelled by existing and emerging applications in economics, biology, genetics, chemistry, physicsand engineering. However diffusions have continuous sample paths so may natural continuous time phenomenarequire more general classes of models. Jump-diffusions have considerable appeal as flexiblefamilies of stochastic models. Bayesian inference for jump-diffusion models motivates new methodologicalchallenges, in particular requires the construction of novel simulation schemes for use within dataaugmentation algorithms and within discretely observed data. In this paper we propose a new methodologyfor exact simulation of jump-diffusion processes. Such method is based on the recently introducedExact Algorithm for exact simulation of diffusions. We also propose a simulation-based method to makelikelihood-based inference for discretely observed jump-diffusions in a Bayesian framework. Simulatedexamples are presented to illustrate the proposed methodology.∗ Apresentador/Speaker32
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