Date of Award

2014

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Xianzheng Huang

Abstract

We consider Bayesian analysis of continuous curve functions in 1D, 2D and 3D spaces. A fundamental feature of the analysis is that it is invariant under a simultaneous warping/re-parameterization of all target curves, as well as translation, rotation and scale of each individual if necessary. We introduce Bayesian models based on a special curve representation named Square Root Velocity Function (SRVF) introduced by Srivastava et al. (2011, IEEE PAMI). A Gaussian process model for the SRVFs of curves is proposed, and suitable prior models such as the Dirichlet distribution are employed for modeling the warping function as a cumulative distribution function. Simulation from posterior distribution is via Markov chain Monte Carlo methods, and credibility regions for mean curves, warping functions as well as nuisance parameters are obtained. Important Monte Carlo techniques such as simulated tempering are employed in order to overcome the problem of getting stuck in a local mode when high dimensional data get involved. We will illustrate the methodology with real data applications as well as simulation studies in 1D, 2D and 3D spaces.

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