Parameterization of Nonstationarity in Stochastic PDE Models

• Activity Number: 101
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Finn Lindgren*+
• Companies: University of Bath
• Keywords: random fields ; stochastic partial differential equations ; Markov random fields ; Bayesian inference

Abstract

Constructing valid non-stationary covariance functions is challenging due to the necessary global conditions for a positive definite function. In contrast, non-stationary stochastic PDE models can be constructed by locally modifying a differential operator. This explicit local structure implicitly generates a valid global covariance structure, which typically does not need to be computed. Instead, the models are expressed via Markov random fields as weights for fixed basis functions. The challenge lies in how to choose the local differential operator, and in how to perform practical parameter inference. Choices include special cases of the Sampson and Guttorp (1992) deformation method, and extend to general operators capable of describing complex patterns of anisotropy. Some of these models can incorporated into direct Bayesian inference packages such as R-INLA, whereas others are more computationally challenging.