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Soils have been heralded as a hidden resource that can be leveraged to mitigate and address some of the major global environmental challenges. Specifically, the organic carbon stored in soils, called soil organic carbon (SOC), can, through proper soil management, help offset fuel emissions, increase food productivity, and improve water quality. As collecting data on SOC are costly and time‐consuming, not much data on SOC are available, although understanding the spatial variability in SOC is of fundamental importance for effective soil management. In this manuscript, we propose a modeling framework that can be used to gain a better understanding of the dependence structure of a spatial process by identifying regions within a spatial domain where the process displays the same spatial correlation range. To achieve this goal, we propose a generalization of the multiresolution approximation (M‐RA) modeling framework of Katzfuss originally introduced as a strategy to reduce the computational burden encountered when analyzing massive spatial datasets. To allow for the possibility that the correlation of a spatial process might be characterized by a different range in different subregions of a spatial domain, we provide the M‐RA basis functions weights with a two‐component mixture prior with one of the mixture components a shrinking prior. We call our approach themixture M‐RA. Application of the mixture M‐RA model to both stationary and nonstationary data show that the mixture M‐RA model can handle both types of data, can correctly establish the type of spatial dependence structure in the data (e.g., stationary versus not), and can identify regions of local stationarity.

In this paper, we propose a stepwise forward selection algorithm for detecting the effects of a set of correlated exposures and their interactions on a health outcome of interest when the underlying relationship could potentially be nonlinear. Though the proposed method is very general, our application in this paper remains to be on analysis of multiple pollutants and their interactions. Simultaneous exposure to multiple environmental pollutants could affect human health in a multitude of complex ways. For understanding the health effects of multiple environmental exposures, it is often important to identify and estimate complex interactions among exposures. However, this issue becomes analytically challenging in the presence of potential nonlinearity in the outcome‐exposure response surface and a set of correlated exposures. Through simulation studies and analyses of test datasets that were simulated as a part of a data challenge in multipollutant modeling organized by the National Institute of Environmental Health Sciences (http://www.niehs.nih.gov/about/events/pastmtg/2015/statistical/), we illustrate the advantages of our proposed method in comparison with existing alternative approaches. A particular strength of our method is that it demonstrates very low false positives across empirical studies. Our method is also used to analyze a dataset that was released from the Health Outcomes and Measurement of the Environment Study as a benchmark beta‐tester dataset as a part of the same workshop.