Abstract:
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Recent advances in remote sensing, specifically 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 high-dimensional and spatially indexed LiDAR signals 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 derived regressors and model residuals to meet statistical assumptions and improve prediction. The dimensionality of the problem is tackled by replacing each spatially referenced signal with its predictive process counterpart. Here a nonseparable spatial covariance function is used to capture within and among signal dependence. The proposed modeling framework is illustrated using LiDAR and spatially coinciding forest inventory data collected on the Penobscot Experimental Forest, Maine.
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