Weibull mixture model for grouped data and pattern identification in spatial and spatial-temporal data.


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Motived by problems in geology, civil engineering, and material science, we develop statistical models and apply statistical tools for characterizing patterns that exist in different types of data. In the first project, we propose the Weibull mixture model to fit the distribution of grain size in continental sediments in geological studies. We use an EM algorithm to fit the model and a bootstrap likelihood ratio test (LRT) to compare different models. The performance of the bootstrap LRT is studied via simulation and is compared with model selection criteria AIC and BIC. Situations where bootstrap LRT is preferred in model selection are discussed. In the second project, we develop robust models for detecting outliers in a large spatial-temporal dataset that contains daily ground deformation values in a New York City tunnel excavation project. Systematic outliers and random outliers are defined and identified using robust spatial kriging models and robust time series models. The residuals from these models are pooled to construct outlier bounds using a moving window technique. The observations whose residuals fall outside of the outlier bounds are flagged as outliers. Artificial outliers are generated and added to the ground deformation data to study the accuracy and stability of the proposed techniques in outlier detection. In the third project, we apply a set of spatial statistical tools for charactering materials at the atomic level with a multivariate three-dimensional atom probe tomography dataset as an example. We use Moran’s I statistic to study the global spatial structure of each atomic feature and apply the local indicator of spatial association (LISA) to study the local spatial regions where high or low values of a given atomic feature exist. LISA is also used for detecting spatial outliers. We then use the local indicator of spatial cross-correlation (LISC) to find where in space high or low levels of two atomic features occur simultaneously. For LISA and LISC, we conduct a conditional permutation test for each location and then compare methods to handle the multiple testing issues. We also discuss the effect of different weight functions and neighborhood selection on the significance of the statistical tests.



Weibull mixture model. Bootstrap likelihood ratio test. Outlier detection. Spatial-temporal. Clustering. Hotspots.