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‣ Man-made structure segmentation using gaussian procesess and wavelet features.
‣ Gaussian averages of interpolated bodies and applications to approximate reconstruction
‣ Efficient High-Dimensional Gaussian Process Regression to calculate the Expected Value of Partial Perfect Information in Health Economic Evaluations
‣ Gaussian Process-Based Bayesian Nonparametric Inference of Population Trajectories from Gene Genealogies
‣ Optimal Bayesian estimation in random covariate design with a rescaled Gaussian process prior
‣ Gaussian Process Regression with Heteroscedastic or Non-Gaussian Residuals
‣ A Constrained Matrix-Variate Gaussian Process for Transposable Data
‣ On Some Asymptotic Properties and an Almost Sure Approximation of the Normalized Inverse-Gaussian Process
‣ Fractional Normal Inverse Gaussian Process
‣ Mixture Gaussian Process Conditional Heteroscedasticity
‣ Varying-coefficient models with isotropic Gaussian process priors
‣ Gaussian Process Kernels for Pattern Discovery and Extrapolation
‣ A Gaussian Process Emulator Approach for Rapid Contaminant Characterization with an Integrated Multizone-CFD Model
‣ Automatically Grading Learners? English Using a Gaussian Process
‣ Gaussian processes for state space models and change point detection
‣ Automatic model construction with Gaussian processes
‣ Bayesian Modeling Using Latent Structures
This dissertation is devoted to modeling complex data from the
Bayesian perspective via constructing priors with latent structures.
There are three major contexts in which this is done -- strategies for
the analysis of dynamic longitudinal data, estimating
shape-constrained functions, and identifying subgroups. The
methodology is illustrated in three different
interdisciplinary contexts: (1) adaptive measurement testing in
education; (2) emulation of computer models for vehicle crashworthiness; and (3) subgroup analyses based on biomarkers.
Chapter 1 presents an overview of the utilized latent structured
priors and an overview of the remainder of the thesis. Chapter 2 is
motivated by the problem of analyzing dichotomous longitudinal data
observed at variable and irregular time points for adaptive
measurement testing in education. One of its main contributions lies
in developing a new class of Dynamic Item Response (DIR) models via
specifying a novel dynamic structure on the prior of the latent
trait. The Bayesian inference for DIR models is undertaken, which
permits borrowing strength from different individuals, allows the
retrospective analysis of an individual's changing ability...
‣ Multivariate Spatial Process Gradients with Environmental Applications
Previous papers have elaborated formal gradient analysis for spatial processes, focusing on the distribution theory for directional derivatives associated with a response variable assumed to follow a Gaussian process model. In the current work, these ideas are extended to additionally accommodate one or more continuous covariate(s) whose directional derivatives are of interest and to relate the behavior of the directional derivatives of the response surface to those of the covariate surface(s). It is of interest to assess whether, in some sense, the gradients of the response follow those of the explanatory variable(s), thereby gaining insight into the local relationships between the variables. The joint Gaussian structure of the spatial random effects and associated directional derivatives allows for explicit distribution theory and, hence, kriging across the spatial region using multivariate normal theory. The gradient analysis is illustrated for bivariate and multivariate spatial models, non-Gaussian responses such as presence-absence and point patterns, and outlined for several additional spatial modeling frameworks that commonly arise in the literature. Working within a hierarchical modeling framework, posterior samples enable all gradient analyses to occur as post model fitting procedures.
; Dissertation