A Bayesian Functional Data Model for Predicting Forest Variables Using High-Dimensional Waveform LiDAR over Large Geographic Domains
Andrew O. Finley, Sudipto Banerjee, Bruce Cook
Departments of Forestry and Geography, Michigan State University, East Lansing, MI, United States; School of Public Health, University of Minnesota, Minneapolis, MN, United States; Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, MD, United States

Recent advances in remote sensing, specifically waveform Light Detection and Ranging (LiDAR) sensors, provide the data needed to quantify forest variables at a fine spatial resolution over large domains. It is common to model the high-dimensional signal vector as a mixture of a relatively small number of Gaussian distributions. The parameters from these Gaussian distributions, or indices derived from the parameters, can then be used as regressors in a regression model. These approaches retain only a small amount of information contained in the signal. Further, it is not known a priori which features of the signal explain the most variability in the response variables. It is possible to more fully exploit the information in the signal by treating it as an object, thus, we define a framework to couple a spatial latent factor model with forest variables using a fully Bayesian functional spatial data analysis. Our proposed modeling framework explicitly: 1) reduces the dimensionality of signals in an optimal way (i.e., preserves the information that describes the maximum variability in response variable); 2) propagates uncertainty in data and parameters through to prediction, and; 3) acknowledges and leverages spatial dependence among the regressors and model residuals to meet statistical assumptions and improve prediction. The dimensionality of the problem is further reduced by replacing each factor's Gaussian spatial process with a reduced rank predictive process. The proposed modeling framework is illustrated using waveform LiDAR and spatially coinciding forest inventory data collected on the Penobscot Experimental Forest, Maine.

Keywords: Spatial process; Predictive process; MCMC; Forestry

Biography: Andrew Finley is an assistant professor at Michigan State University with a joint appointment in the Departments of Forestry and Geography, his research interests include developing methodologies for monitoring and modeling environmental processes, Bayesian statistics, spatial statistics, and statistical computing.