  Recent advancements in remote sensing technology, specifically Light
Detection and Ranging (LiDAR) sensors, provide the data needed to quantify
forest characteristics at a fine spatial resolution over large geographic
domains. From an inferential standpoint, there is interest in prediction and
interpolation of the often sparsely sampled and spatially misaligned LiDAR
signals and forest variables. We propose a fully process-based Bayesian
hierarchical model for above ground biomass (AGB) and LiDAR signals. The
process-based framework offers richness in inferential capabilities, e.g.,
inference on the entire underlying processes instead of estimates only at
pre-specified points. Key challenges we obviate include misalignment between
the AGB observations and LiDAR signals and the high-dimensionality in the model
emerging from LiDAR signals in conjunction with the large number of spatial
locations. We offer simulation experiments to evaluate our proposed models and
also apply them to a challenging dataset comprising LiDAR and spatially
coinciding forest inventory variables collected on the Penobscot Experimental
Forest (PEF), Maine. Our key substantive contributions include AGB data
products with associated measures of uncertainty for the PEF and, more broadly,
a methodology that should find use in a variety of current and upcoming forest
variable mapping efforts using sparsely sampled remotely sensed
high-dimensional data.
