Hierarchical modeling of space-time dendroclimatic fields: Comparing a frequentist and a Bayesian approach

Environmental processes, including climatic impacts in cold regions, are typically acting at multiple spatial and temporal scales. Hierarchical models are a flexible statistical tool that allows for decomposing spatiotemporal processes in simpler components connected by conditional probabilistic relationships. This article reviews two hierarchical models that have been applied to tree-ring proxy records of climate to model their space–time structure: STEM (Spatio-Temporal Expectation Maximization) and BARCAST (Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time). Both models account for spatial and temporal autocorrelation by including latent spatiotemporal processes, and they both take into consideration measurement and model errors, while they differ in their inferential approach. STEM adopts the frequentist perspective, and its parameters are estimated through the expectation-maximization (EM) algorithm, with uncertainty assessed through bootstrap resampling. BARCAST is developed in the Bayesian framework, and relies on Markov chain Monte Carlo (MCMC) algorithms for sampling values from posterior probability distributions of interest. STEM also explicitly includes covariates in the process model definition. As hierarchical modeling keeps contributing to the analysis of complex ecological and environmental processes, proxy reconstructions are likely to improve, thereby providing better constraints on future climate change scenarios and their impacts over cold regions.