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

ABSTRACT

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.

KEYWORDS:

• Tree rings
• STEM
• BARCAST
• climate reconstruction
• autocorrelation

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Following Gelfand and Smith (1990), brackets denote probability density functions of random variables. For example, [X] is the marginal distribution of the unidimensional random variable X, while [X |Y] and [X,Y] represent the conditional and joint distribution of X and Y, respectively. Bold characters are adopted for multivariate random variables.

Additional information

Funding

M.C. was supported by the PRIN EphaStat Project (project 20154X8K23, https://sites.google.com/site/ephastat) provided by the Italian Ministry for Education, University and Research. F.B. was supported, in part, by the U.S. National Science Foundation under grants AGS-P2C2-1401381 and AGS-P2C2-1502379. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the opinions or policies of the funding agencies.