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The Gaussian process is an indispensable tool for spatial data analysts. The onset of the “big data” era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics.

The frequent use of antibiotics contributes to antibiotic resistance in bacteria, resulting in an increase in infections that are difficult to treat. Livestock are commonly administered antibiotics in their feed, but there is current interest in raising animals that are only administered antibiotics during active infections. Staphylococcus aureus (SA) is a common pathogen of both humans and livestock raised for human consumption. SA has achieved high levels of antibiotic resistance, but the origins and locations of resistance selection are poorly understood. We determined the prevalence of SA and MRSA in conventional and antibiotic-free (AF) meat products, and also measured rates of antibiotic resistance in these isolates. We isolated SA from raw conventional turkey, chicken, beef, and pork samples and also from AF chicken and turkey samples. We found that SA contamination was common, with an overall prevalence of 22.6% (range of 2.8-30.8%) in conventional meats and 13.0% (range of 12.5-13.2%) in AF poultry meats. MRSA was isolated from 15.7% of conventional raw meats (range of 2.8-20.4%) but not from AF-free meats. The degree of antibiotic resistance in conventional poultry products was significantly higher vs AF poultry products for a number of different antibiotics, and while multi-drug resistant strains were relatively common in conventional meats none were detected in AF meats. The use of antibiotics in livestock contributes to high levels of antibiotic resistance in SA found in meat products. Our results support the use of AF conditions for livestock in order to prevent antibiotic resistance development in SA.

Understanding spatial and temporal dynamics of soil water within fields is critical for effective variable rate irrigation (VRI) management. The objectives of this study were to develop VRI zones, manage irrigation rates within VRI zones, and examine temporal differences in soil volumetric water content (VWC) from irrigation events via soil sensors across zones. Five irrigation zones were delineated after two years (2016 and 2017) of yield and evapotranspiration (ET) data collection. Soil sensors were placed within each zone to give real time data of VWC values and assist in irrigation decisions within a 23 ha field of winter wheat (Triticum aestivum ‘UI Magic’) near Grace, Idaho, USA (2019). Cumulative irrigation rates among zones ranged from 236 to 298 mm. Although a statistical comparison could not be made, the irrigation rates were 0.6 to 21% less than an estimated uniform grower standard practice (GSP) irrigation approach. Based on soil sensor data, crop water stress was avoided with VRI management in all but Zone 3. Thus, this simple approach to VRI zone delineation and VWC monitoring has the potential to reduce irrigation, such as this study, on average by 12% and should be evaluated in other site-years to assess its viability.

Elevated nitrate from human activity causes ecosystem and economic harm globally. The factors that control the spatiotemporal dynamics of riverine nitrate concentration remain difficult to describe and predict. We analyzed nitrate concentration from 4450 sites throughout France to group sites that exhibit similar trend and seasonal behaviors during 2010–2017 and relate these dynamics to catchment characteristics. We employed a latent-variable, Bayesian mixture of harmonic regressions model to infer site clustering based on multi-year trend and annual cycle amplitude and phase. We examined clustering patterns and relationships among nitrate level, trend, and seasonality parameters. Cluster membership probabilities were governed by continuous, latent variables that were informed with seven classes of covariates encompassing geology, hydrology, and land use. To relate interpretable parameters to the covariates, we modeled amplitude and phase separately in a novel framework employing a bivariate phase regression with the projected normal distribution. The analysis identified regional regimes of nitrate dynamics, including trend classifications. This approach can reveal general patterns that transcend small-scale heterogeneity, complementing site-level assessments to inform regional- to national-level progress in water quality. Supplementary materials accompanying this paper appear on-line.

Modern digital data production methods, such as computer simulation and remote sensing, have vastly increased the size and complexity of data collected over spatial domains. Analysis of these large spatial datasets for scientific inquiry is typically carried out using the Gaussian process. However, nonstationary behavior and computational requirements for large spatial datasets can prohibit efficient implementation of Gaussian process models. To perform computationally feasible inference for large spatial data, we consider partitioning a spatial region into disjoint sets using hierarchical clustering of observations and finite differences as a measure of dissimilarity. Intuitively, directions with large finite differences indicate directions of rapid increase or decrease and are, therefore, appropriate for partitioning the spatial region. Spatial contiguity of the resulting clusters is enforced by only clustering Voronoi neighbors. Following spatial clustering, we propose a nonstationary Gaussian process model across the clusters, which allows the computational burden of model fitting to be distributed across multiple cores and nodes. The methodology is primarily motivated and illustrated by an application to the validation of digital temperature data over the city of Houston as well as simulated datasets. Supplementary materials for this article are available online.

Irrigation is responsible for 80–90% of freshwater consumption in the USA. However, excess water demand, drought, declining groundwater levels, and water quality degradation all threaten future water supplies. In an effort to better understand how to efficiently use water resources, this analysis seeks to quantify the effect of soil water at various depths on the eventual crop yield at the end of a season as a lagged effect of space and time. As a novel modeling contribution, we propose a multiple spatiotemporal lagged model for crop yield to identify critical water times and patterns that can increase the crop yield per drop of water used. Because the crop yield data consist of nearly 20,000 observations, we propose the use of a nearest neighbor Gaussian process to facilitate computation. In applying the model to soil water and yield in Grace, Idaho, for the 2016 season, results indicate that soil moisture in the 0–0.3 m depth of soil was most correlated with crop yield earlier in the season (primarily during May and June), while the soil moisture at the 0.3–1.2 m depth was more correlated with crop yield later in the season around mid-June to mid-July. These results are specific to a crop of winter wheat under center-pivot irrigation, but the model could be used to understand relationships between water and yield for other crops and irrigation systems.

The high mountain regions of Asia contain more glacial ice than anywhere on the planet outside of the polar regions. Because of the large population living in the Indus watershed region who are reliant on melt from these glaciers for fresh water, understanding the factors that affect glacial melt along with the impacts of climate change on the region is important for managing these natural resources. While there are multiple climate data products (e.g., reanalysis and global climate models) available to study the impact of climate change on this region, each product will have a different amount of skill in projecting a given climate variable, such as precipitation. In this research, we develop a spatially varying mixture model to compare the distribution of precipitation in the High Mountain Asia region as produced by climate models with the corresponding distribution from in situ observations from the Asian Precipitation—Highly Resolved Observational Data Integration Towards Evaluation (APHRODITE) data product. Parameter estimation is carried out via a computationally efficient Markov chain Monte Carlo algorithm. Each of the estimated climate distributions from each climate data product is then validated against APHRODITE using a spatially varying Kullback–Leibler divergence measure. Supplementary materials accompanying this paper appear online.

The presence and establishment of a tree species at a particular spatial location is influenced by multiple physiological and environmental filters such as propagule pressure (seed availability), light and moisture availability, and slope and elevation. However, a less understood environmental filter to species-specific establishment is competition or facilitation between dominant tree species. For example, certain tree species may compete for resources at spatial locations where such resources are scarce while less competition may occur at resource-rich areas. Using data from the Forest Inventory and Analysis (FIA) program of the United States Department of Agriculture (USDA) Forest Service, we develop a multivariate spatial Bernoulli model to investigate the space-varying relationship between extant tree species in Utah. Additionally, we propose a novel modeling strategy that explains the spatially varying relationships by regressing the associated between-species correlation matrix on available covariate data. Positive definite conditions of the covariate-varying correlation matrix are ensured by defining the regression in terms of the unique partial correlation matrix. Results indicate that correlations between species are dependent upon elevation.

Extreme heat, or persistently high temperatures in the form of heatwaves, adversely impacts human health. To study such effects, risk maps are a common epidemiological tool that is used to identify regions and populations that are more susceptible to these negative outcomes; however, the negative health effects of high temperatures are manifested differently between different segments of the population. We propose a novel, hierarchical marked point process model that merges multiple health outcomes into an overall heat risk map. Specifically, we consider health outcomes of heat-stress-related emergency service calls and mortalities across the city of Houston, Texas. We show that combining multiple health outcomes leads to a broader understanding of the spatial distribution of heat risk than a single health outcome.

Summary The Lyon–Fedder–Mobarry global magnetosphere–ionosphere coupled model LFM‐MIX is used to study Sun–Earth interactions by simulating geomagnetic storms. This work focuses on relating the multifidelity output from LFM‐MIX to field observations of ionospheric conductance. Given a set of input values and solar wind data, LFM‐MIX numerically solves the magnetohydrodynamic equations and outputs a bivariate spatiotemporal field of ionospheric energy and flux. Of particular interest here are LFM‐MIX input settings required to match corresponding output with field observations. To estimate these input settings, a multivariate spatiotemporal statistical LFM‐MIX emulator is constructed. The statistical emulator leverages the multiple fidelities such that the less computationally demanding yet lower fidelity LFM‐MIX is used to provide estimates of the higher fidelity output. The higher fidelity LFM‐MIX output is then used for calibration by using additive and non‐linear discrepancy functions.