Physical Sciences and Mathematics Commons^™

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

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In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Radiation Exposure Calibration Of The Al2o3:C With Radium-226 And Cesium-137 Using The Osl Method, Selma Tepeli Aydin

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Optically stimulated luminescence (OSL) dosimetry was utilized to calibrate Al₂O₃:C powder dosimeters, available commercially as the nanoDot® from Landauer Inc., and compare the dosimeter response to radium-226 (²²⁶Ra) and cesium-137 (¹³⁷Cs). The signal from the OSL was quantified using a microSTARii^® OSL reader also produced by Landauer Inc. Dose-response curves were developed for ²²⁶Ra and ¹³⁷Cs experiments (5 dosimeters each) at thirteen absorbed doses. Individual dosimeter response was tracked by serial number. Linear regression analysis was performed to determine if there were significant differences between the intercepts of the …

A Framework For Statistical Modeling Of Wind Speed And Wind Direction, Eva Murphy

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Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. This dissertation aims to provide a modeling framework for studying the variation of wind speed and wind direction. To this end, three projects are conducted to address some of the key issues for modeling wind vectors.\\

First, a conditional decomposition approach is developed to model the joint distribution of wind speed and direction. Specifically, the …

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

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Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Green On The Map - The Influence Of Conservation Easements On The Naturalness Of Landscapes In The United States, Nakisha Fouch

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Large protected areas have long been the cornerstone of conservation biology, however, in an era branded by the human dominance of ecosystems, regional landscape structure and function are often a consequence of accumulated land-use decisions that may or may not include a nod to conservation planning. With underrepresentation of habitats in publicly protected areas, attention has focused on the function of alternative land conservation mechanisms. Private conservation easements (CEs) have proliferated in the United States, yet assessing landscape-level function is confounded by holder and donor intent, national and regional policy, regional landscape contexts, varying extents, resolution, and temporal scale. Over …

Statistical Methods For Modern Threats, Brandon Lumsden

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More than ever before, technology is evolving at a rapid pace across the broad spectrum of biological sciences. As data collection becomes more precise, efficient, and standardized, a demand for appropriate statistical modeling grows as well. Throughout this dissertation, we examine a variety of new age data arising from modern technology of the 21st century. We begin by employing a suite of existing statistical techniques to address research questions surrounding three medical conditions presenting in public health sciences. Here we describe the techniques used, including generalized linear models and longitudinal models, and we summarize the significant associations identified between research …

Lindley Processes With Correlated Changes, John Grant

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This dissertation studies a Lindley random walk model when the increment process driving the walk is strictly stationary. Lindley random walks govern customer waiting times in many queueing models and several natural and business processes, including snow depths, frozen soil depths, inventory quantities, etc. Probabilistic properties of a Lindley process with time-correlated stationary changes are explored. We provide a streamlined argument that the process admits a limiting stationary distribution when the mean of the incremental changes is negative and that the Lindley process is strictly stationary when starting from this stationary distribution. The Markov characteristics of the process are explored …

Learning Graphical Models Of Multivariate Functional Data With Applications To Neuroimaging, Jiajing Niu

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This dissertation investigates the functional graphical models that infer the functional connectivity based on neuroimaging data, which is noisy, high dimensional and has limited samples. The dissertation provides two recipes to infer the functional graphical model: 1) a fully Bayesian framework 2) an end-to-end deep model.

We first propose a fully Bayesian regularization scheme to estimate functional graphical models. We consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019).. We then propose a regularization strategy via the graphical horseshoe. We compare both Bayesian approaches to the frequentist functional graphical lasso, and compare the …

Advanced High Dimensional Regression Techniques, Yuan Yang

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This dissertation focuses on developing high dimensional regression techniques to analyze large scale data using both Bayesian and frequentist approaches, motivated by data sets from various disciplines, such as public health and genetics. More specifically, Chapters 2 and Chapter 4 take a Bayesian approach to achieve modeling and parameter estimation simultaneously while Chapter 3 takes a frequentist approach. The main aspects of these techniques are that they perform variable selection and parameter estimation simultaneously, while also being easily adaptable to large-scale data. In particular, by embedding a logistic model into traditional spike and slab framework and selecting of proper prior …

Development Of A Reverse Engineered, Parameterized, And Structurally Validated Computational Model To Identify Design Parameters That Influence American Football Faceguard Performance, William Ferriell

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Traumatic brain injury (TBI) continues to have the greatest incidence among athletes participating in American football. The headgear design research community has focused on developing accurate computational and experimental analysis techniques to better assess the ability of headgear technology to attenuate impacts and protect athletes from TBI. Despite efforts to innovate the headgear system, minimal progress has been made to innovate the faceguard. Although the faceguard is not the primary component of the headgear system that contributes to impact attenuation, faceguard performance metrics, such as weight, structural stiffness, and visual field occlusions, have been linked to athlete safety. To improve …

Penalized Estimation Of Autocorrelation, Xiyan Tan

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This dissertation explored the idea of penalized method in estimating the autocorrelation (ACF) and partial autocorrelation (PACF) in order to solve the problem that the sample (partial) autocorrelation underestimates the magnitude of (partial) autocorrelation in stationary time series. Although finite sample bias corrections can be found under specific assumed models, no general formulae are available. We introduce a novel penalized M-estimator for (partial) autocorrelation, with the penalty pushing the estimator toward a target selected from the data. This both encapsulates and differs from previous attempts at penalized estimation for autocorrelation, which shrink the estimator toward the target value of zero. …

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

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Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …

Some Improved Markov Chain Convergence Rates, Fun Choi John Chan

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Explicit convergence rates to equilibrium are established for non reversible Markov chains not having an atom via coupling methods. We consider two Markov chains having the same transition function but different initial conditions on the same probability space, that is, a coupling. A random time is constructed so that subsequent to the random time the two processes are identical. Exploiting a shadowing condition, we show that it is possible to bound the tail distribution of the random time using only one of the chains. This bound gives the convergence rate to equilibrium for the Markov chain. The method is then …

Groundwork For The Development Of Gpu Enabled Group Testing Regression Models, Paul Cubre

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In this dissertation, we develop novel techniques that allow for the regression analysis of data emerging from group testing processes and set the groundwork for graphic processing units (GPU) enabled implementations. Group testing primarily occurs in clinical laboratories, where it is used to quickly and cheaply diagnose patients. Typically, group testing tests a pooled specimen--several specimens combined into one sample--instead of testing individual specimens one-by-one. This method reduces costs by using fewer tests when the disease prevalence is low. Due to recent advances in diagnostic technology, group testing protocols were extended to incorporate multiplex assays, which are diagnostic tests that, …

A Contribution To The Statistical Analysis Of Climate-Wildfire Interaction In Northern California, Adam Diaz

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Wildfires are extreme weather events that exist at the interface of atmospheric, ecological, and human processes. Ongoing anthropogenic climate change is expected to impact the distribution, frequency, and behavior of wildfires on a grand scale, however the exact nature of this change remains shrouded in a great deal of uncertainty. This study takes a statistical approach to the question over the fire-prone Northern California region of the western United states. Climate model projections are analyzed to investigate changes in a major driver of fire weather in the region. The relationship between wildfire severity and climate factors is then explored separately, …

Objective Bayesian Analysis On The Quantile Regression, Shiyi Tu

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The dissertation consists of two distinct but related research projects. First of all, we study the Bayesian analysis on the two-piece location-scale models, which contain several well-known sub-distributions, such as the asymmetric Laplace distribution, the skewed normal distribution, and the skewed Student-t distribution. The use of two-piece location-scale models is an attractive method to model non-symmetric data. From a practical point of view, a prior with some objective information may be more reasonable due to the lack of prior information in many applied situations. It has been shown that several common used objective priors, such as the Jeffreys prior, result …

Quantile Regression For Climate Data, Dilhani Marasinghe

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Quantile regression is a developing statistical tool which is used to explain the relationship between response and predictor variables. This thesis describes two examples of climatology using quantile regression.Our main goal is to estimate derivatives of a conditional mean and/or conditional quantile function. We introduce a method to handle autocorrelation in the framework of quantile regression and used it with the temperature data. Also we explain some properties of the tornado data which is non-normally distributed. Even though quantile regression provides a more comprehensive view, when talking about residuals with the normality and the constant variance assumption, we would prefer …

Convergence Of A Reinforcement Learning Algorithm In Continuous Domains, Stephen Carden

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In the field of Reinforcement Learning, Markov Decision Processes with a finite number of states and actions have been well studied, and there exist algorithms capable of producing a sequence of policies which converge to an optimal policy with probability one. Convergence guarantees for problems with continuous states also exist. Until recently, no online algorithm for continuous states and continuous actions has been proven to produce optimal policies. This Dissertation contains the results of research into reinforcement learning algorithms for problems in which both the state and action spaces are continuous. The problems to be solved are introduced formally as …

Unifying Specific Climate Research With A Molar Climate Measure: A Situational Affordances Approach, Alice Brawley

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Organizational climate - briefly, the shared perceptions of a workplace - was originally studied as a molar concept, but this approach generally lacked focus and thus resulted in unmanageable measures. Organizational climate research has been subdivided into many areas of specific climate research focusing on particular organizational factors or outcomes, such as safety or customer service (Schneider, Ehrhart, & Macey, 2013). While the study of specific climates has been and remains worthwhile, recent literature in the area has called for a return to the molar or global conceptualization of organizational climate (Kuenzi & Schminke, 2009; Schneider et al., 2013). In …

Genetic Algorithm Techniques In Climate Changepoint Problems, Shanghong Li

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The first part of this dissertation studies genetic algorithms as a means of estimating the number of changepoints and their locations in a climatic time series. Such methods bypass classical subsegmentation algorithms, which sometimes yield suboptimal conclusions. Minimum description length techniques are introduced. These techniques require optimizing an objective function over all possible changepoint numbers and location times. Our general objective functions allow for correlated data, reference station aspects, and/or non-normal marginal distributions, all common features of climate time series. As an exhaustive evaluation of all changepoint configurations is not possible, the optimization is accomplished via a genetic algorithm that …

L1 Methods For Shrinkage And Correlation, Jie Shen

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This dissertation explored the idea of L1 norm in solving two statistical problems including multiple linear regression and diagnostic checking in time series. In recent years L1 shrinkage methods have become popular in linear regression as they can achieve simultaneous variable selection and parameter estimation. Their objective functions containing a least squares term and an L1 penalty term which can produce sparse solutions (Fan and Li, 2001). Least absolute shrinkage and selection operator (Lasso) was the first L1 penalized method proposed and has been widely used in practice. But the Lasso estimator has noticeable bias and is inconsistent for variable …

Extreme Value Theory In Periodic Time Series, Zhiyun Gong

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Extreme data points are important in environmental, financial, and insurance settings. In this work, we consider two topics on extremes from environmental data. Many environmental time series have a seasonal structure. The first part presents an approach to identify the rare events of such series based on time series residuals. Here, periodic autoregressive moving-average models are applied to describe the series. The methods justify the application of classical peaks over threshold methods to estimated versions of the one-step-ahead prediction errors of the series. Such methods enable the seasonal means, variances, and autocorrelations of the series to be taken into account. …

Count Time Series And Discrete Renewal Processes, James Livsey

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Most data collected over time has some degree of periodicity (i.e. seasonally varying
traits). Climate, stock prices, football season, energy consumption, wildlife sightings, and
holiday sales all have cyclical patterns. It should come as no surprise that models that
incorporate periodicity are paramount in the study of time series.
The following work devises time series models for counts (integer-values) that are periodic
and stationary. Foundational work is rst done in constructing a stationary periodic
discrete renewal process (SPDRP). The dynamics of the SPDRP are mathematically interesting
and have many modeling applications, expositions largely unexplored here. This work
develops a SPDRP …

Objective Bayesian Hypothesis Testing And Estimation For The Risk Ratio In A Correlated 2x2 Table With Structural Zero, Xiaohua Bai

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We illustrate the construction of an objective Bayesian hypothesis testing and point estimation for the risk ratio in a correlated 2x2 table with structural zero. We solve the problem using Bayesian method through the reference prior, and corresponding posterior distribution of the risk ratio can be derived. Then combined the intrinsic discrepancy, an invariant inforamtion-based loss function, provides an integrated objective Bayesian solution to both hypothesis testing and point estimation problems.

Robust And Efficient Regression, Qi Zheng

All Dissertations

This dissertation aims to address two problems in regression
analysis. One problem is the model selection and robust parameter estimation in high dimensional linear regressions. The other is concerning developing a robust and efficient estimator in nonparametric regressions.
In Chapter 1, we introduce the robust and efficient regression analysis, discuss those two interesting problems and our motivations, and present several exciting results.
We propose a novel robust penalized method for high dimensional linear regression in Chapter 2. Asymptotic properties are established and a data-driven procedure is developed to select adaptive penalties. We show it is the very first estimator to …

Bayesian Hypothesis Testing And Variable Selection In High Dimensional Regression, Min Wang

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This dissertation consists of three distinct but related research projects. First of all, we study the Bayesian approach to model selection in the class of normal regression models. We propose an explicit closed-form expression of the Bayes factor with the use of Zellner's g-prior and the beta-prime prior for g. Noting that linear models with a growing number of unknown parameters have recently gained increasing popularity in practice, such as the spline problem, we shall thus be particularly interested in studying the model selection consistency of the Bayes factor under the scenario in which the dimension of the parameter space …

Error Covariance Matrix Estimation In High Dimensional Approximate Factor Models Using Adaptive Thresholding: A Simulation Study, Paul Chimenti

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Approximate factor models are popular in finance and economics. A key to effectively utilizing such a model is to accurately estimate the error covariance matrix. Errors related to certain predictors are expected to be correlated and this must be modeled effectively. Adaptive thresholding is a method for estimating the error covariance matrix of such a model. This method is described in detail and a simulation study sheds light on the behavior of this method under different sample sizes and parameterizations.

Asymptotics For The Arc Length Of A Multivariate Time Series And Its Applications As A Measure Of Risk, Tharanga Wickramarachchi

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The necessity of more trustworthy methods for measuring the risk (volatility) of financial assets has come to the surface with the global market downturn This dissertation aims to propose sample arc length of a time series, which provides a measure of the overall magnitude of the one-step-ahead changes over the observation time period, as a new approach for quantifying the risk. The Gaussian functional central limit theorem is proven under finite second moment conditions. Without loss of generality we consider equally spaced time series when first differences of the series follow a variety of popular stationary models including autoregressive moving …

Objective Bayesian Inference On The Common Mean Of Normal Distributions, Shiyi Tu

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One of the oldest problems in statistical area is to make inference on a common mean of several different normal populations with unknown and probably unequal variances. There are several different ways to make inference on the common mean. The most common methods are point estimation, hypothesis testing, and interval estimation. Point estimation uses sample data to calculate a single value serving as a best guess for the unknown population mean. Hypothesis testing assumes all populations have the same mean as the null hypothesis. Interval estimation is an interval of possible values of the unknown mean.
In this paper, we …

New Results In Multivariate Time Series With Applications, Nan Su

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This dissertation presents some new results in stationary multivariate time series.
The asymptotic properties of the sample autocovariance are established, that is, we derive a multivariate version of Bartlett's Classic Formula.
The estimation of the autocovariance function plays a crucial role in time series analysis,
in particular for the identification problem.
Explicit formula for vector autoregressive $(p)$ and vector moving average $(q)$ processes are presented as examples.
We also address linear processes driven by non-independent errors,
a feature that permits consideration of multivariate GARCH processes.
We next compare several techniques to discriminate
two multivariate stationary signals. The compared methods include …