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Retrospective Mixed Model and Propensity Score Methods for Case Control Data
(2015-09-28)
In chapter one a Liability Threshold Mixed Linear Model (LTMLM) association statistic is introduced for ascertained case-control studies that increases power vs. existing mixed model methods for diseases with low prevalence, ...
Statistical Methods for Analyzing Complex Spatial and Missing Data
(2015-12-04)
In chapter 1, we develop a novel two-dimensional wavelet decomposition to decompose spatial surfaces into different frequencies without imposing any restrictions on the form of the spatial surface. We illustrate the ...
Robust Semi-Parametric Inference in Semi-Supervised Settings
(2016-05-17)
In this dissertation, we consider semi-parametric estimation problems under semi-supervised (SS) settings, wherein the available data consists of a small or moderate sized labeled data (L), and a much larger unlabeled data ...
Statistical Methods for Estimating the Effects of Multi-Pollutant Exposures in Children's Health Research
(2016-09-15)
We develop statistical strategies to explore how time-varying exposures to heavy metal mixtures affects cognition and cognitive trajectories in children. In chapter 1, we develop a Bayesian model, called Lagged Kernel ...
Hypothesis Testing and Model Selection for Complex Data
(2017-05-15)
In this dissertation, we propose methodology for hypothesis testing in statistical genetics and model selection in networks. In chapters 1 and 2, we introduce new methods to tackle difficulties in hypothesis testing for ...
Bayesian Statistical Framework for High-Dimensional Count Data and its Application in Microbiome Studies
(2017-05-10)
High-dimensional count data arising from multinomial sampling is ubiquitous in microbiome studies. This dissertation aims to develop flexible Bayesian framework to model high-dimensional count data, which provides reliable ...
Methods for Estimating Hidden Structure and Network Transitions in Genomics
(2017-05-04)
The explosion of data arising from advances in high throughput sequencing has allowed scientists to study genomics in far greater detail. However, this high resolution picture of cells often makes it difficult to see the ...
Methods for High-Dimensional Inference in Genetic Association Studies
(2017-05-10)
Genetic association studies are frequently characterized by high-dimensional datasets containing rare and weak signals. To detect these signals, it is important to choose inference methods that are both robust and powerful ...
Statistical Methods for the Analysis of Observational Data With Multiple Correlated Outcomes
(2017-09-11)
In this work, we consider three problems in applied statistics motivated by complex datasets, with approaches from both Frequentist and Bayesian paradigms. Chapter 2 is motivated by case-control data collected for the Army ...