Practical Space-Time Random Fields Based on Stochastic PDES

• Activity Number: 601
• Type: Invited
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Finn Lindgren*+
• Companies: Norwegian University of Science and Technology
• Keywords: Markov random fields ; stochastic partial differential equations ; computational methods ; space-time models

Abstract

The traditional approach to random field models, which defines them through positive definite covariance functions, typically results in computationally expensive algorithms when the size of the domain or the data is large. Kernel based convolution fields are easier to construct, but do not inherently reduce the computational burden for statistical inference. An alternative is to specify the model through a stochastic partial differential equation (SPDE). Since the theory can be daunting, a tempting solution would be to deduce the corresponding kernels or covariance functions, and apply one of the common approximation techniques, such as tapering. However, calculating these functions is a distraction that is computationally expensive, especially when compared to a more direct use of the SPDE. A good alternative is to directly use the SPDE to construct a Markov random field approximation to the true random field. The resulting model inherits its physical interpretability from the SPDE, and its Markovian structure allows for the cheap solution of much larger problems than can be solved using the traditional methods. The approach is illustrated with global environmetric data sets.