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Abstract Numerous modelling techniques exist to estimate abundance of plant and animal populations. The most accurate methods account for multiple complexities found in ecological data, such as observational biases, spatial autocorrelation, and species correlations. There is, however, a lack of user‐friendly and computationally efficient software to implement the various models, particularly for large data sets.We developed thespAbundance Rpackage for fitting spatially explicit Bayesian single‐species and multi‐species hierarchical distance sampling models, N‐mixture models, and generalized linear mixed models. The models within the package can account for spatial autocorrelation using Nearest Neighbour Gaussian Processes and accommodate species correlations in multi‐species models using a latent factor approach, which enables model fitting for data sets with large numbers of sites and/or species.We provide three vignettes and three case studies that highlightspAbundancefunctionality. We used spatially explicit multi‐species distance sampling models to estimate density of 16 bird species in Florida, USA, an N‐mixture model to estimate black‐throated blue warbler (Setophaga caerulescens) abundance in New Hampshire, USA, and a spatial linear mixed model to estimate forest above‐ground biomass across the continental USA.spAbundanceprovides a user‐friendly, formula‐based interface to fit a variety of univariate and multivariate spatially explicit abundance models. The package serves as a useful tool for ecologists and conservation practitioners to generate improved inference and predictions on the spatial drivers of abundance in populations and communities. 

Abstract 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 remote portion of Interior Alaska. 

Abstract 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.