This work deals with multivariate spatial categorical data that arise from observations of Wisconsin’s historical forests sampled in the Wisconsin Public Land Survey (PLS). To identify and map forest community types across the landscape, we propose a finite mixture model with a Markov random field for the latent labels to classify forest communities while accounting for spatial correlation. We develop a stochastic approximation algorithm using Markov chain Monte Carlo (MCMC) for estimating the parameters of this model. I will discuss results of model fitting and forest community mapping for the historical PLS data and validate our approach through a simulation study. For the large PLS dataset, the finite mixture models with spatially correlated labels are computationally feasible and perform better on holdout data than models without a spatial correlation component. More broadly, motivated by stochastic approximation algorithms such as the one used in the PLS data analysis, we propose a novel control variate method for reducing the variance and increasing the efficiency of MCMC simulations involving deterministic sweep Markov chains. We establish theoretically that this new control variate approach outperforms competing methodology in several Gibbs sampling settings and further demonstrate the validity of our results via a simulation study.
Stephen Berg is a PhD student at the University of Wisconsin - Madison advised by Jun Zhu and Murray Clayton. His specialization is in spatial statistics, and his research interests include environmental statistics, statistical computing, and Markov random field models.
For more information on Stephen: https://stephenberg.github.io/