An Improved Bayesian Semiparametric Model for Palaeoclimate Reconstruction: Cross-validation Based Model Assessment

Fossil-based palaeoclimate reconstruction is an important area of ecological science that has gained momentum in the backdrop of the global climate change debate. The hierarchical Bayesian paradigm provides an interesting platform for studying such important scientific issue. However, our cross-validation based assessment of the existing Bayesian hierarchical models with respect to two modern proxy data sets based on chironomid and pollen, respectively, revealed that the models are inadequate for the data sets. In this paper, we model the species assemblages (compositional data) by the zero-inflated multinomial distribution, while modelling the species response functions using Dirichlet process based Gaussian mixtures. This modelling strategy yielded significantly improved performances, and a formal Bayesian test of model adequacy, developed recently, showed that our new model is adequate for both the modern data sets. Furthermore, combining together the zero-inflated assumption, Importance Resampling Markov Chain Monte Carlo (IRMCMC) and the recently developed Transformation-based Markov Chain Monte Carlo (TMCMC), we develop a powerful and efficient computational methodology.