Bayesian multi-resolution modeling for spatially replicated data sets with application to forest biomass data

Analysts in the natural and environmental sciences often encounter spatially referenced data sets arising from designs that are spatially replicated, where we have a set of main plots, each subdivided into several subplots. Spatial variation, therefore, possibly exists at two resolutions: macro-level variation between the main plots and micro-level variation between the subplots within each main plot. Scientific interest centers around estimating the underlying spatial associations and effects at multiple resolutions. These objectives introduce fresh challenges in statistical modeling, especially with regard to constructing rich association structures that yield valid probability models. We outline a spatial-process based versatile methodological framework to accomplish such modeling within a hierarchical Bayesian paradigm. We illustrate the proposed method using forest biomass data from the Forest Inventory and Analysis program of the United States Department of Agriculture (USDA) Forest Service.