Spatial Joint Species Distribution Modeling using Dirichlet Processes

Species distribution models usually attempt to explain presence-absence or abundance of a species at a site in terms of the environmental features (socalled abiotic features) present at the site. Historically, such models have considered species individually. However, it is well-established that species interact to influence presence-absence and abundance (envisioned as biotic factors). As a result, there has been substantial recent interest in joint species distribution models with various types of response, e.g., presence-absence, continuous and ordinal data. Such models incorporate dependence between species response as a surrogate for interaction. The challenge we focus on here is how to address such modeling in the context of a large number of species (e.g., order 102) across sites numbering in the order of 102 or 103 when, in practice, only a few species are found at any observed site. Again, there is some recent literature to address this; we adopt a dimension reduction approach. The novel wrinkle we add here is spatial dependence. That is, we have a collection of sites over a relatively small spatial region so it is anticipated that species distribution at a given site would be similar to that at a nearby site. Specifically, we handle dimension reduction through Dirichlet processes joined with spatial dependence through Gaussian processes. We use both simulated data and a plant communities dataset for the Cape Floristic Region (CFR) of South Africa to demonstrate our approach. The latter consists of presence-absence measurements for 639 tree species on 662 locations. Through both data examples we are able to demonstrate improved predictive performance using the foregoing specification

Modeling Space-Time Data Using Stochastic Differential Equations

This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Business Administratio

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This manuscript develops a class of highly scalable Nearest Neighbor Gaussian Process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive United States Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods