Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field

TL;DR

This paper develops a Bayesian non-stationary spatial model for annual precipitation in southern Norway, leveraging multiple years of data and SPDE-based methods to improve estimation accuracy and address parameter identifiability issues.

Contribution

It introduces a non-stationary spatial model with replicates, enhancing estimation precision and prior robustness using R-INLA and SPDE frameworks.

Findings

Replicate data improves parameter estimation accuracy.

The model effectively captures non-stationary spatial dependence.

Simulation studies validate the model's statistical properties.

Abstract

Estimation of stationary dependence structure parameters using only a single realisation of the spatial process, typically leads to inaccurate estimates and poorly identified parameters. A common way to handle this is to fix some of the parameters, or within the Bayesian framework, impose prior knowledge. In many applied settings, stationary models are not flexible enough to model the process of interest, thus non-stationary spatial models are used. However, more flexible models usually means more parameters, and the identifiability problem becomes even more challenging. We investigate aspects of estimation of a Bayesian non-stationary spatial model for annual precipitation using observations from multiple years. The model contains replicates of the spatial field, which increases precision of the estimates and makes them less prior sensitive. Using R-INLA, we analyse precipitation data from southern Norway, and investigate statistical properties of the replicate model in a simulation study. The non-stationary spatial model we explore belongs to a recently introduced class of stochastic partial differential equation (SPDE) based spatial models. This model class allows for non-stationary models with explanatory variables in the dependence structure. We derive conditions to facilitate prior specification for these types of non-stationary spatial models.