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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 remote portion of Interior Alaska.

 

Multivariate spatially oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for each variable and associations among the different dependent variables. Multivariate latent spatial process models have proved effective in driving statistical inference and rendering better predictive inference at arbitrary locations for the spatial process. High‐dimensional multivariate spatial data, which are the theme of this article, refer to data sets where the number of spatial locations and the number of spatially dependent variables is very large. The field has witnessed substantial developments in scalable models for univariate spatial processes, but such methods for multivariate spatial processes, especially when the number of outcomes are moderately large, are limited in comparison. Here, we extend scalable modeling strategies for a single process to multivariate processes. We pursue Bayesian inference, which is attractive for full uncertainty quantification of the latent spatial process. Our approach exploits distribution theory for the matrix‐normal distribution, which we use to construct scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models that deliver inference over a high‐dimensional parameter space including the latent spatial process. We illustrate the computational and inferential benefits of our algorithms over competing methods using simulation studies and an analysis of a massive vegetation index data set.

 

We develop a Bayesian model–based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key distinction from the small area estimation setting is that we analyze finite populations referenced by their geographic coordinates. Specifically, we consider a two‐stage sampling design in which the primary units are geographic regions, the secondary units are point‐referenced locations, and the measured values are assumed to be a partial realization of a spatial process. Estimation of finite population quantities from geostatistical models does not account for sampling designs, which can impair inferential performance, whereas design‐based estimates ignore the spatial dependence in the finite population. We demonstrate by using simulation experiments that process‐based finite population sampling models improve model fit and inference over models that fail to account for spatial correlation. Furthermore, the process‐based models offer richer inference with spatially interpolated maps over the entire region. We reinforce these improvements and demonstrate scalable inference for groundwater nitrate levels in the population of California Central Valley wells by offering estimates of mean nitrate levels and their spatially interpolated maps.

 

Abstract Background The 2010 Deepwater Horizon (DWH) oil spill involved thousands of workers and volunteers to mitigate the oil release and clean-up after the spill. Health concerns for these participants led to the initiation of a prospective epidemiological study (GuLF STUDY) to investigate potential adverse health outcomes associated with the oil spill response and clean-up (OSRC). Characterizing the chemical exposures of the OSRC workers was an essential component of the study. Workers on the four oil rig vessels mitigating the spill and located within a 1852 m (1 nautical mile) radius of the damaged wellhead [the Discoverer Enterprise (Enterprise), the Development Driller II (DDII), the Development Driller III (DDIII), and the Helix Q4000] had some of the greatest potential for chemical exposures. Objectives The aim of this paper is to characterize potential personal chemical exposures via the inhalation route for workers on those four rig vessels. Specifically, we presented our methodology and descriptive statistics of exposure estimates for total hydrocarbons (THCs), benzene, toluene, ethylbenzene, xylene, and n-hexane (BTEX-H) for various job groups to develop exposure groups for the GuLF STUDY cohort. Methods Using descriptive information associated with the measurements taken on various jobs on these rig vessels and with job titles from study participant responses to the study questionnaire, job groups [unique job/rig/time period (TP) combinations] were developed to describe groups of workers with the same or closely related job titles. A total of 500 job groups were considered for estimation using the available 8139 personal measurements. We used a univariate Bayesian model to analyze the THC measurements and a bivariate Bayesian regression framework to jointly model the measurements of THC and each of the BTEX-H chemicals separately, both models taking into account the many measurements that were below the analytic limit of detection. Results Highest THC exposures occurred in TP1a and TP1b, which was before the well was mechanically capped. The posterior medians of the arithmetic mean (AM) ranged from 0.11 ppm (‘Inside/Other’, TP1b, DDII; and ‘Driller’, TP3, DDII) to 14.67 ppm (‘Methanol Operations’, TP1b, Enterprise). There were statistical differences between the THC AMs by broad job groups, rigs, and time periods. The AMs for BTEX-H were generally about two to three orders of magnitude lower than the THC AMs, with benzene and ethylbenzene measurements being highly censored. Conclusions Our results add new insights to the limited literature on exposures associated with oil spill responses and support the current epidemiologic investigation of potential adverse health effects of the oil spill.