Date of Completion

8-3-2020

Embargo Period

8-3-2022

Keywords

Boundary Analysis, Spatial Models, Spatiotemporal Models

Major Advisor

Dipak K. Dey

Associate Advisor

Ming-Hui Chen

Associate Advisor

Xiaojing Wang

Associate Advisor

Vladimir Podznyakov

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

In this dissertation we focus on developing a framework for detecting zones of rapid change within a surface that is spatially or spatiotemporally indexed, which is termed as wombling. This is considered under two different approaches featuring a semi-parametric model and a model based parametric setup. The second approach starts with a Gaussian process specification on the spatial or spatiotemporal component. We focus on applying the developed framework to build models for analyzing spatiotemporally referenced insurance data arising from losses due to automobile collision in the state of Connecticut, in the year 2008. For the semi-parametric models we adopt a penalization based approach which imposes a penalty on the graph Laplacian that promotes spatial clustering. A coordinate descent algorithm is developed to estimate model parameters. The approach is extended further to encompass various members of the exponential dispersion family. We operate under a double generalized linear model framework featuring joint modeling of the mean and dispersion, coupled with spatial uncertainty quantification. A geographic boundary analysis framework is then developed to detect zones characterizing significant spatial signal in the response. For the parametric setup we resort to Bayesian hierarchical modeling of the spatial and spatiotemporally referenced insurance data. We develop a model based inferential wombling or boundary analysis framework for performing curvilinear wombling on open and closed curves within the spatial surface, while quantifying their evolution in time with respect to the spatial signal. This is facilitated by developing gradient and curvature processes arising from a Gaussian process specification on the response surface. Necessary and sufficient conditions are derived that ensure existence of such derivative processes. We operate within a hierarchical modeling framework that allows us to specify this dependence of the response on policy level covariates within the data, while also allowing us to infer about topological characteristics of the residual spatial surface. These are supplemented with synthetic illustrations under both Gaussian and latent Gaussian specifications and real data applications that demonstrate the inferential capability of our proposed framework.

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