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A key challenge in spatial data science is the analysis for massive spatially‐referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance matrices that lack computationally exploitable structures. Recent developments in spatial statistics offer a variety of massively scalable approaches. Bayesian inference and hierarchical models, in particular, have gained popularity due to their richness and flexibility in accommodating spatial processes. Our current contribution is to provide computationally efficient exact algorithms for spatial interpolation of massive data sets using scalable spatial processes. We combine low‐rank Gaussian processes with efficient sparse approximations. Following recent work by Zhang et al. (2019), we model the low‐rank process using a Gaussian predictive process (GPP) and the residual process as a sparsity‐inducing nearest‐neighbor Gaussian process (NNGP). A key contribution here is to implement these models using exact conjugate Bayesian modeling to avoid expensive iterative algorithms. Through the simulation studies, we evaluate performance of the proposed approach and the robustness of our models, especially for long range prediction. We implement our approaches for remotely sensed light detection and ranging (LiDAR) data collected over the US Forest Service Tanana Inventory Unit (TIU) in a remotemore »portion of Interior Alaska.

Changing forest disturbance regimes and climate are driving accelerated tree mortality across temperate forests. However, it remains unknown if elevated mortality has induced decline of tree populations and the ecological, economic, and social benefits they provide. Here, we develop a standardized forest demographic index and use it to quantify trends in tree population dynamics over the last two decades in the western United States. The rate and pattern of change we observe across species and tree size-distributions is alarming and often undesirable. We observe significant population decline in a majority of species examined, show decline was particularly severe, albeit size-dependent, among subalpine tree species, and provide evidence of widespread shifts in the size-structure of montane forests. Our findings offer a stark warning of changing forest composition and structure across the western US, and suggest that sustained anthropogenic and natural stress will likely result in broad-scale transformation of temperate forests globally.

Occupancy modelling is a common approach to assess species distribution patterns, while explicitly accounting for false absences in detection–nondetection data. Numerous extensions of the basic single‐species occupancy model exist to model multiple species, spatial autocorrelation and to integrate multiple data types. However, development of specialized and computationally efficient software to incorporate such extensions, especially for large datasets, is scarce or absent.

Joint modeling of spatially oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for massive data sets with variables measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of its reliance on iterative estimation algorithms. This article develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that obviate iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process in a hierarchical model. We illustrate the computational and inferential benefits of these models using simulation studies and analysis of a vegetation index data set with spatially dependent observations numbering in the millions.