Bayesian palaeoclimate reconstruction from zero-inflated count-compositional pollen data: A case study of Lago Grande di Monticchio in southern Italy
Bayesian palaeoclimate reconstruction from fossil pollen counts relies on a modern pollen-climate calibration data set to infer the pollen-climate relationships used to reconstruct past climates. While geographically large calibration data sets improve coverage of climate space and reduce unreliable extrapolation, they also introduce substantial heterogeneity, structural zeros, and complex pollen-climate relationships. We propose a Bayesian modular framework for palaeoclimate reconstruction from count-compositional pollen data that addresses these challenges, and provides coherent uncertainty quantification. The framework employs the zero-and-$N$-inflated multinomial logistic-normal distribution to describe the compositional pollen counts coupled with Bayesian additive regression tree priors to model the nonlinear effects and interactions among the climate covariates. Inference is formulated through a cut posterior distribution that modularises the analysis into forward and reconstruction modules. The forward module is fitted once using a large modern calibration data set and its posterior uncertainty is subsequently propagated to reconstruct climate variables from fossil pollen counts. For the reconstruction module, we develop and compare three inverse posterior sampling schemes. Simulation studies and empirical validation on the modern data set demonstrate that a combination of sampling importance resampling with a multiple imputation technique and a continuous uniform prior over the domain of the modern climate variables achieves the best predictive performance, with well-calibrated uncertainty quantification for the climate reconstruction. In our motivating case study, we further illustrate the proposed methodology by reconstructing a three-dimensional climate vector from fossil pollen records collected at Lago Grande di Monticchio in southern Italy.