Modelling Spatial Compositional Data: Reconstructions of past land cover and uncertainties

TL;DR

This paper develops a hierarchical Bayesian model using GMRFs and MCMC to reconstruct past land cover in Europe over 6,000 years, providing uncertainty quantification and validation against known data.

Contribution

It introduces a novel hierarchical GMRF-based model with efficient MCMC for reconstructing past land cover and a new method for joint confidence regions to quantify uncertainty.

Findings

Model accurately reconstructs known land cover structures.

Reconstruction method effectively combines pollen data and vegetation models.

Uncertainty quantification method provides reliable confidence regions.

Abstract

In this paper, we construct a hierarchical model for spatial compositional data, which is used to reconstruct past land-cover compositions (in terms of coniferous forest, broadleaved forest, and unforested/open land) for five time periods during the past $6\,000$ years over Europe. The model consists of a Gaussian Markov Random Field (GMRF) with Dirichlet observations. A block updated Markov chain Monte Carlo (MCMC), including an adaptive Metropolis adjusted Langevin step, is used to estimate model parameters. The sparse precision matrix in the GMRF provides computational advantages leading to a fast MCMC algorithm. Reconstructions are obtained by combining pollen-based estimates of vegetation cover at a limited number of locations with scenarios of past deforestation and output from a dynamic vegetation model. To evaluate uncertainties in the predictions a novel way of constructing joint confidence regions for the entire composition at each prediction location is proposed. The hierarchical model's ability to reconstruct past land cover is evaluated through cross validation for all time periods, and by comparing reconstructions for the recent past to a present day European forest map. The evaluation results are promising and the model is able to capture known structures in past land-cover compositions.