Gathering information about forest variables is an expensive and arduous activity. As such, directly collecting the data required to produce high-resolution maps over large spatial domains is infeasible. Next generation collection initiatives of remotely sensed Light Detection and Ranging (LiDAR) data are specifically aimed at producing complete-coverage maps over large spatial domains. Given that LiDAR data and forest characteristics are often strongly correlated, it is possible to make use of the former to model, predict, and map forest variables over regions of interest. This entails dealing with the high-dimensional (~102) spatially dependent LiDAR outcomes over a large number of locations (~105-106). With this in mind, we develop the Spatial Factor Nearest Neighbor Gaussian Process (SF-NNGP) model, and embed it in a two-stage approach that connects the spatial structure found in LiDAR signals with forest variables. We provide a simulation experiment that demonstrates inferential and predictive performance of the SF-NNGP, and use the two-stage modeling strategy to generate complete-coverage maps of forest variables with associated uncertainty over a large region of boreal forests in interior Alaska.

中文翻译：

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高维大空间数据的空间因子模型：在森林变量映射中的应用

收集有关森林变量的信息是一项昂贵且艰巨的活动。因此，直接收集在大空间域上生成高分辨率地图所需的数据是不可行的。下一代遥感光探测和测距（LiDAR）数据收集计划专门旨在生成大空间域的完整覆盖地图。鉴于 LiDAR 数据和森林特征通常密切相关，因此可以利用前者对感兴趣区域的森林变量进行建模、预测和映射。这需要处理大量位置（~105-106）上的高维（~102）空间相关 LiDAR 结果。考虑到这一点，我们开发了空间因子最近邻高斯过程 (SF-NNGP) 模型，并将其嵌入到将 LiDAR 信号中发现的空间结构与森林变量连接起来的两阶段方法中。我们提供了一个模拟实验，展示了 SF-NNGP 的推理和预测性能，并使用两阶段建模策略生成森林变量的完整覆盖图，以及阿拉斯加内陆大片北方森林的相关不确定性。