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Climate field reconstructions (CFRs) attempt to estimate spatiotemporal fields of climate variables in the past using climate proxies such as tree rings, ice cores, and corals. Data assimilation (DA) methods are a recent and promising new means of deriving CFRs that optimally fuse climate proxies with climate model output. Despite the growing application of DA-based CFRs, little is understood about how much the assimilated proxies change the statistical properties of the climate model data. To address this question, we propose a robust and computationally efficient method, based on functional data depth, to evaluate differences in the distributions of two spatiotemporal processes. We apply our test to study global and regional proxy influence in DA-based CFRs by comparing the background and analysis states, which are treated as two samples of spatiotemporal fields.We find that the analysis states are significantly altered from the climate-model-based background states due to the assimilation of proxies. Moreover, the difference between the analysis and background states increases with the number of proxies, even in regions far beyond proxy collection sites. Our approach allows us to characterize the added value of proxies, indicating where and when the analysis states are distinct from the background states. Supplementary materials for this article are available online. 

In this paper, we propose a novel Bayesian group regularization method based on the spike and slab Lasso priors for jointly estimating multiple graphical models. The proposed method can be used to estimate common sparsity structure underlying the graphical models while capturing potential heterogeneity of the precision matrices corresponding to those models. Our theoretical results show that the proposed method enjoys the optimal rate of convergence in L-infinity norm for estimation consistency and has a strong structure recovery guarantee even when the signal strengths over different graphs are heterogeneous. Through simulation studies and an application to the capital bike-sharing network data, we demonstrate the competitive performance of our method compared to existing alternatives. 

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.