Work

A Parameterization of Anisotropic Gaussian Fields with Penalized Complexity Priors

Year: 2026

Type: article

Abstract: Gaussian random fields (GFs) are fundamental tools in spatial modeling and can be represented flexibly and efficiently as solutions to stochastic partial differential equations (SPDEs). The SPDEs depend on specific parameters, which enforce various field behaviors and can be estimated using Bayesian inference. However, even under in-fill asymptotics, the likelihood only provides limited insights into the covariance structure. In response, it is essential to leverage priors to achieve appropriate, meaningful covariance structures in the posterior. This study introduces a smooth, invertible parameterization of the correlation length and diffusion matrix of an anisotropic GF and constructs penalized complexity (PC) priors for the model when the parameters are constant in space. The formulated prior is weakly informative, effectively penalizing complexity by pushing the correlation range toward infinity and the anisotropy to zero. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Source: Journal of the American Statistical Association

DOI: 10.1080/01621459.2026.2670016

Authors: L. Llamazares-Elias, J. Latz, F. Lindgren

Institutions: Maxwell Institute for Mathematical Sciences, University of Edinburgh, University of Manchester

Language: English

Topic: Spatial and Panel Data Analysis

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Funders: Heriot-Watt University, Scottish Funding Council, University of Edinburgh, Engineering and Physical Sciences Research Council

Award: EPSRC Centre for Doctoral Training in Mathematical Modelling, Analysis and Computation (MAC-MIGS)