B0873
Title: Penalized complexity priors for stochastic partial differential equations
Authors: Liam Llamazares - University of Edinburgh (United Kingdom) [presenting]
Finn Lindgren - University of Edinburgh (United Kingdom)
Jonas Latz - Heriot-Watt University (United Kingdom)
Abstract: Gaussian random fields (GRFs) are fundamental in spatial modeling and can be represented flexibly and efficiently by stochastic partial differential equations (SPDEs). The SPDEs depend on specific parameters, which enforce various field behaviors and can be estimated using Bayesian inference. However, the likelihood typically only provides limited insights into the covariance structure under in-fill asymptotics. In response, it is essential to leverage priors to achieve appropriate, meaningful covariance structures in the posterior. An innovative parameterization of a non-stationary GRF is introduced using its correlation length and diffusion matrix. Penalized complexity is then extended priors to the model, first when parameters are independent of space and then to spatially dependent parameters. The cornerstone of this extension is the spectral density which is defined for non-stationary fields and is proven to possess desirable properties. The formulated prior is weakly informative and effectively penalizes complexity by pushing the correlation range toward infinity and the anisotropy to zero.
