Reconstruction of past European land cover from pollen data: using spatial statistics and Crank-Nicolson Monte Carlo

Abstract: Given a pollen data set from Europe over a time period, the aim is to reconstruct the past land cover by interpolating from the pollen data values to a continuous map. The data is on compositional form with three vegetation categories; coniferous forest, broadleaved forest and open land. Reconstruction will be based on a Gaussian Markov random field with separable spatio-temporal structure for the covariance matrix. The spatio-temporal covariance matrix is constructed by Kronecker products which simplifies many matrix computations. The field and parameters for the model are estimated by Markov Chain Monte Carlo, with a Crank Nicolson Langevin proposal to estimate the spatio-temporal field. Crank Nicolson Langevin method works well, although implementation could be technical with a lot of details. Convergence for some of the model parameters is slow with bad mixing. The average compositional distance for the reconstruction and the validation set was 0.71. The model was better at finding temporal structure rather than spatial. Reconstructions from this model could be used as input to other models such as \citep{Strandberg} to investigate how anthropogenic deforestation, and other changes in nature, impacts climate change.