A Bayesian Functional Data Model for Predicting Forest Variables Using High-Dimensional Waveform LiDAR Over Large Geographic Domains

• Activity Number: 99
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: JABES-Journal of Agricultural, Biological, and Environmental Statistics
• Author(s): Andrew Oliver Finley*+ and Sudipto Banerjee and Bruce Cook
• Companies: Michigan State University and University of Minnesota and NASA Goddard Space Flight Center
• Keywords: MCMC ; predictive process ; spatial GLM ; spatial process ; Hierarchical model

Abstract

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. 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.