A Hierarchical Model for Quantifying Forest Variables Over Large Heterogeneous Landscapes With Uncertain Forest Areas

We are interested in predicting one or more continuous forest variables (e.g., biomass, volume, age) at a fine resolution (e.g., pixel level) across a specified domain. Given a definition of forest/nonforest, this prediction is typically a two-step process. The first step predicts which locations are forested. The second step predicts the value of the variable for only those forested locations. Rarely is the forest/nonforest status predicted without error. However, the uncertainty in this prediction is typically not propagated through to the subsequent prediction of the forest variable of interest. Failure to acknowledge this error can result in biased estimates of forest variable totals within a domain. In response to this problem, we offer a modeling framework that will allow propagation of this uncertainty. Here we envision two latent processes generating the data. The first is a continuous spatial process while the second is a binary spatial process. The continuous spatial process controls the spatial association structure of the forest variable of interest, while the binary process indicates presence of a possible nonzero value for the forest variable at a given location. The proposed models are applied to georeferenced National Forest Inventory (NFI) data and spatially coinciding remotely sensed predictor variables. Due to the large number of observed locations in this dataset we seek dimension reduction not just in the likelihood, but also for unobserved stochastic processes. We demonstrate how a low-rank predictive process can be adapted to our setting and reduce the dimensionality of the data and ease the computational burden.