The project focuses on methods to retrieve signals in spatial data that are possibly masked due to measurement errors. Specifically, the investigator proposes to establish unbiased parameter estimates and optimal predictions for spatially correlated data with errors present in both predictors and responses, and then apply the solutions to paleoclimate reconstruction to achieve a faithful representation of the past climate. The results from the proposed work will take both the spatial correlation and errors-in-variables into account to uncover the true relationship between the response and explanatory variables. The bias and the asymptotic behavior of the parameter estimates and the optimality of predictions in different senses under various measurement error structures are investigated. Besides, a new practical method for estimating the variance-covariance matrix of measurement errors for data with no replicates is proposed.
The primary impact of this project is to provide practical statistical tools to correct the effects of errors-in-variables in spatial data analysis. Once the results are applied to paleoclimate reconstructions, they will solve a long standing problem concerning the amplitudes of past climate that plays a central role in understanding the dynamics of the climate system. In addition to climatology, the proposed methods can be generally applied to a variety of other disciplines such as seismology, environmetrics, atmospheric sciences and public health studies, where data are usually spatially correlated and contain substantial noise. However, the broader impacts of the proposed activities are multiple. A key aspect of this proposal is the integration of research and teaching, which will be achieved by proposing specific projects for students during the teaching of classes on measurement errors and on spatial statistics.
The signals in spatial data can be possibly masked due to measurement errors. The paleoclimate reconstruction based on proxies such as tree-ring, ice core, and other indirect observations suffers from the big amount of measurement errors in proxies. We developed statistical models to capture the underlying structure of the data with measurement errors taken into account, and identified the appropriate model for paleoclimate reconstruction that is adequate to capture various error structures in different proxies and corrects the attenuation bias caused by the inherent noise in proxies. The PI’s work ranges from the flexible nonparametric modeling of correlation structure in spatial data to multivariate spatial data modeling, from a self-normalization procedure to substitute the subsampling or bootstrap while making inference for spatial data, to copula methods for modeling the non-Gaussian correlated data, and to a rigorous paleoclimate reconstruction by carefully investigating the most appropriate memory length in the time series. The PI’s research has made significant contributions to both the statistical methodology development and understanding of climate and environmental sciences. The precise estimation of past climate together with its uncertainty quantification provide important insights into the dynamics of past climate change that, in turn, have implications for the future. The interdisciplinary research between statistics and paleoclimatology benefits both communities, provides excellent research examples in statistical class, and introduces new research topics and research directions for PhD students.
