Statistics and Probability Commons^™

Time Series Analysis: A New Look At Some Old Problems, Ferebee Tunno

All Dissertations

This dissertation gives a comprehensive report of my doctoral research in time series analysis from summer 2006 to spring 2009. It is comprised of two main efforts: interval estimation for an autoregressive parameter and arc length tests for equivalent ARIMA dynamics. Such problems are traditional in statistics, but three new theorems and several simulations are presented here that help elucidate new ways to handle them.

Investigations Of Variable Importance Measures Within Random Forests, Andrew C. Merrill

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Random Forests (RF) (Breiman 2001; Breiman and Cutler 2004) is a completely nonparametric statistical learning procedure that may be used for regression analysis and. A feature of RF that is drawing a lot of attention is the novel algorithm that is used to evaluate the relative importance of the predictor/explanatory variables. Other machine learning algorithms for regression and classification, such as support vector machines and artificial neural networks (Hastie et al. 2009), exhibit high predictive accuracy but provide little insight into predictive power of individual variables. In contrast, the permutation algorithm of RF has already established a track record for …

Resampling-Based Multiple Hypothesis Testing With Applications To Genomics: New Developments In The R/Bioconductor Package Multtest, Houston N. Gilbert, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

The multtest package is a standard Bioconductor package containing a suite of functions useful for executing, summarizing, and displaying the results from a wide variety of multiple testing procedures (MTPs). In addition to many popular MTPs, the central methodological focus of the multtest package is the implementation of powerful joint multiple testing procedures. Joint MTPs are able to account for the dependencies between test statistics by effectively making use of (estimates of) the test statistics joint null distribution. To this end, two additional bootstrap-based estimates of the test statistics joint null distribution have been developed for use in the …

A Class Of Semiparametric Mixture Cure Survival Models With Dependent Censoring, Megan Othus, Yi Li, Ram C. Tiwari

Harvard University Biostatistics Working Paper Series

No abstract provided.

Application Of Time-To-Event Methods In The Assessment Of Safety In Clinical Trials, Kelly L. Moore, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Since randomized controlled trials (RCT) are typically designed and powered for efficacy rather than safety, power is an important concern in the analysis of the effect of treatment on the occurrence of adverse events (AE). These outcomes are often time-to-event outcomes which will naturally be subject to right-censoring due to early patient withdrawals. In the analysis of the treatment effect on such an outcome, gains in efficiency, and thus power, can be achieved by exploiting covariate information. We apply the targeted maximum likelihood methodology to the estimation of treatment specific survival at a fixed end point for right-censored survival outcomes. …

Interval Estimation For The Difference In Paired Areas Under The Roc Curves In The Absence Of A Gold Standard Test, Hsin-Neng Hsieh, Hsiu-Yuan Su, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve (AUC). A gold standard test on the true disease status is required to estimate the AUC. However, a gold standard test may sometimes be too expensive or infeasible. Therefore, in many medical research studies, the true disease status of the subjects may remain unknown. Under the normality assumption on test results from each disease group of subjects, using the expectation-maximization …

Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs.

The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent …

Collaborative Targeted Maximum Likelihood Estimation, Mark J. Van Der Laan, Susan Gruber

U.C. Berkeley Division of Biostatistics Working Paper Series

Collaborative double robust targeted maximum likelihood estimators represent a fundamental further advance over standard targeted maximum likelihood estimators of causal inference and variable importance parameters. The targeted maximum likelihood approach involves fluctuating an initial density estimate, (Q), in order to make a bias/variance tradeoff targeted towards a specific parameter in a semi-parametric model. The fluctuation involves estimation of a nuisance parameter portion of the likelihood, g. TMLE and other double robust estimators have been shown to be consistent and asymptotically normally distributed (CAN) under regularity conditions, when either one of these two factors of the likelihood of the data is …

A Semi-Parametric Two-Part Mixed-Effects Heteroscedastic Transformation Model For Correlated Right-Skewed Semi-Continuous Data, Huazhen Lin, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In longitudinal or hierarchical structure studies, we often encounter a semi-continuous variable that has a certain proportion of a single value and a continuous and skewed distribution among the rest of values. In the paper, we propose a new semi-parametric two-part mixed-effects transformation model to fit correlated skewed semi-continuous data. In our model, we allow the transformation to be non-parametric. Fitting the proposed model faces computational challenges due to intractable numerical integrations. We derive the estimates for the parameter and the transformation function based on an approximate likelihood, which has high order accuracy but less computational burden. We also propose …

Xprime: A Method Incorporating Expert Prior Information Into Motif Exploration, Rachel Lynn Poulsen

Theses and Dissertations

One of the primary goals of active research in molecular biology is to better understand the process of transcription regulation. An important objective in understanding transcription is identifying transcription factors that directly regulate target genes. Identifying these transcription factors is a key step toward eliminating genetic diseases or disease susceptibilities that are encoded inside deoxyribonucleic acid (DNA). There is much uncertainty and variation associated with transcription factor binding sites, requiring these sites to be represented stochastically. Although typically each transcription factor prefers to bind to a specific DNA word, it can bind to different variations of that DNA word. In …

Composite Likelihood Bayesian Information Criteria For Model Selection In High Dimensional Data, X Gao, Peter Xuekun Song

The University of Michigan Department of Biostatistics Working Paper Series

For high-dimensional data set with complicated dependency structures, the full likelihood approach often renders to intractable computational complexity. This imposes di±culty on model selection as most of the traditionally used information criteria require the evaluation of the full likelihood. We propose a composite likelihood version of the Bayesian information criterion (BIC) and establish its consistency property for the selection of the true underlying model. Under some mild regularity conditions, the proposed BIC is shown to be selection consistent, where the number of potential model parameters is allowed to increase to in¯nity at a certain rate of the sample size. Simulation …

Longitudinal Image Analysis Of Tumor/Brain Change In Contrast Uptake Induced By Radiation, Xiaoxi Zhang, Tim Johnson, Rod Little, Yue Cao

The University of Michigan Department of Biostatistics Working Paper Series

This work is motivated by a quantitative Magnetic Resonance Imaging study of the differential tumor/healthy tissue change in contrast uptake induced by radiation. The goal is to determine the time in which there is maximal contrast uptake, a surrogate for permeability, in the tumor relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang, Johnson, Little, and Cao (2008a and 2008b) discuss two parallel approaches to “denoise” a single image of change in contrast uptake from baseline to a single follow-up visit of interest. In this work we explore the longitudinal profile of the tumor/healthy …

Joint Multiple Testing Procedures For Graphical Model Selection With Applications To Biological Networks, Houston N. Gilbert, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Gaussian graphical models have become popular tools for identifying relationships between genes when analyzing microarray expression data. In the classical undirected Gaussian graphical model setting, conditional independence relationships can be inferred from partial correlations obtained from the concentration matrix (= inverse covariance matrix) when the sample size n exceeds the number of parameters p which need to estimated. In situations where n < p, another approach to graphical model estimation may rely on calculating unconditional (zero-order) and first-order partial correlations. In these settings, the goal is to identify a lower-order conditional independence graph, sometimes referred to as a ‘0-1 graphs’. For either choice of graph, model selection may involve a multiple testing problem, in which edges in a graph are drawn only after rejecting hypotheses involving (saturated or lower-order) partial correlation parameters. Most multiple testing procedures applied in previously proposed graphical model selection algorithms rely on standard, marginal testing methods which do not take into account the joint distribution of the test statistics derived from (partial) correlations. We propose and implement a multiple testing framework useful when testing for edge inclusion during graphical model selection. Two features of our methodology include (i) a computationally efficient and asymptotically valid test statistics joint null distribution derived from influence curves for correlation-based parameters, and (ii) the application of empirical Bayes joint multiple testing procedures which can effectively control a variety of popular Type I error rates by incorpo- rating joint null distributions such as those described here (Dudoit and van der Laan, 2008). Using a dataset from Arabidopsis thaliana, we observe that the use of more sophisticated, modular approaches to multiple testing allows one to identify greater numbers of edges when approximating an undirected graphical model using a 0-1 graph. Our framework may also be extended to edge testing algorithms for other types of graphical models (e.g., for classical undirected, bidirected, and directed acyclic graphs).

A Snapshot Algorithm For Linear Feedback Flow Control Design, Benjamin T. Dickinson, Belinda A. Batten, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The control of fluid flows has many applications. For micro air vehicles, integrated flow control designs could enhance flight stability by mitigating the effect of destabilizing air flows in their low Reynolds number regimes. However, computing model based feedback control designs can be challenging due to high dimensional discretized flow models. In this work, we investigate the use of a snapshot algorithm proposed in Ref. 1 to approximate the feedback gain operator for a linear incompressible unsteady flow problem on a bounded domain. The main component of the algorithm is obtaining solution snapshots of certain linear flow problems. Numerical results …

A Hidden Markov Model Based Approach To Detect Rogue Access Points, Gayathri Shivaraj

Electrical & Computer Engineering Theses & Dissertations

One of the most challenging security concerns for network administrators is the presence of Rogue access points. The challenge is to detect and disable a Rogue access point before it can cause hazardous damage to the network. This thesis proposes a statistically based approach to detect Rogue access points using a Hidden Markov Model, which is applied to passively measure packet-header data collected at a gateway router or any monitoring point. This approach utilizes variations in packet inter-arrival time to differentiate between authorized access points and Rouge access points. This approach used the inter-arrival time of a packet as a …

Will Quants Rule The (Legal) World?, Edward K. Cheng

Vanderbilt Law School Faculty Publications

Professor Ian Ayres, in his new book, Super Crunchers, details the brave new world of statistical prediction and how it has already begun to affect our lives. For years, academic researchers have known about the considerable and at times surprising advantages of statistical models over the considered judgments of experienced clinicians and experts. Today, these models are emerging all over the landscape. Whether the field is wine, baseball, medicine, or consumer relations, they are vying against traditional experts for control over how we make decisions. For the legal system, the take-home of Ayres's book and the examples he describes is …

The Robustness Of Confidence Intervals For The Mean Of Delta Distribution, Mathew Anthony Cantos Rosales

Dissertations

The delta distribution is a mixture of a lognormal distribution and a distribution degenerate at zero. Interval estimators of the mean of delta distribution were proposed and examined under full assumption of the model. In this dissertation, robustness of these estimators is studied by comparing coverage properties when the data are contaminated. Simulation models have been considered to accommodate two types of contaminants: (1) data from lognormal distribution with higher level of skewness and (2) data from similar skewed distribution such as gamma, Weibull or Birnbaum-Saunders distributions with the same mean and variance as the original lognormal distribution. In addition, …

The Importance Of Scale For Spatial-Confounding Bias And Precision Of Spatial Regression Estimators, Christopher J. Paciorek

Harvard University Biostatistics Working Paper Series

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias …

Smoking Enhances Risk For New External Genital Warts In Men, Dorothy J. Wiley, David Elashoff, Emmanuel V. Masongsong, Diane M. Harper

Dartmouth Scholarship

Repeat episodes of HPV-related external genital warts reflect recurring or new infections. No study before has been sufficiently powered to delineate how tobacco use, prior history of EGWs and HIV infection affect the risk for new EGWs. Behavioral, laboratory and examination data for 2,835 Multicenter AIDS Cohort Study participants examined at 21,519 semi-annual visits were evaluated. Fourteen percent (391/2835) of men reported or were diagnosed with EGWs at 3% (675/21,519) of study visits. Multivariate analyses showed smoking, prior episodes of EGWs, HIV infection and CD4+ T-lymphocyte count among the infected, each differentially influenced the risk for new EGWs.

Detecting Near-Earth Objects Using Cross-Correlation With A Point Spread Function, Anthony P. O'Dell

Theses and Dissertations

This thesis describes a process to help discover Near-Earth Objects (NEOs) of larger than 140 meters in diameter from ground based telescopes. The process involves using Nyquist sampling rate to take data from a ground-based telescope and measuring the atmospheric seeing parameter, r₀, at the time of data collection. r0 is then used to create a point spread function (PSF) for a NEO at the visual magnitude limit of the telescope and exposure time. This PSF is cross-correlated with the Nyquist sampling rate image from the telescope to reduce the noise and therefore increase the detection probability of …

Measuring Skill Importance In Women's Soccer And Volleyball, Michelle L. Allan

Theses and Dissertations

The purpose of this study is to demonstrate how to measure skill importance for two sports: soccer and volleyball. A division I women's soccer team filmed each home game during a competitive season. Every defensive, dribbling, first touch, and passing skill was rated and recorded for each team. It was noted whether each sequence of plays led to a successful shot. A hierarchical Bayesian logistic regression model is implemented to determine how the performance of the skill affects the probability of a successful shot. A division I women's volleyball team rated each skill (serve, pass, set, etc.) and recorded rally …

Analysis Of Randomized Comparative Clinical Trial Data For Personalized Treatment Selections, Tianxi Cai, Lu Tian, Peggy H. Wong, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Correlated Binary Regression Using Orthogonalized Residuals, Richard C. Zink, Bahjat F. Qaqish

COBRA Preprint Series

This paper focuses on marginal regression models for correlated binary responses when estimation of the association structure is of primary interest. A new estimating function approach based on orthogonalized residuals is proposed. This procedure allows a new representation and addresses some of the difficulties of the conditional-residual formulation of alternating logistic regressions of Carey, Zeger & Diggle (1993). The new method is illustrated with an analysis of data on impaired pulmonary function.

Demonstration And Verification Of A Broad Spectrum Anomalous Dispersion Effects Tool For Index Of Refraction And Optical Turbulence Calculations, J. Jean Cohen

Theses and Dissertations

An atmospheric optical turbulence strength model with a broad wavelength range of 355nm (ultraviolet) to 8.6m (radio frequencies) has been created at AFIT and implemented into the High Energy Laser End-to-End Operational Simulation tool (HELEEOS). This modeling and simulation tool is a first principles atmospheric propagation and characterization model. Within HELEEOS lies the High-Resolution Transmission Molecular Absorption (HITRAN) database, containing 1,734,469 spectral lines for 37 different molecules as of version 12.0 (2004). HITRAN affords HELEEOS incredible accuracy for electromagnetic (EM) propagation prediction. A full understanding of optical turbulence is needed to successfully predict EM radiation propagation, particularly within the application …

Robust Sensitivity Analysis For The Joint Improvised Explosive Device Defeat Organization (Jieddo) Proposal Selection Model, Christina J. Willy

Theses and Dissertations

Throughout Operations Iraqi Freedom and Enduring Freedom, the Department of Defense (DoD) faced challenges not experienced in our previous military operations. The enemy’s unwavering dedication to the use of improvised explosive devices (IEDs) against the coalition forces continues to challenge the day-to-day operations of the current war. The Joint Improvised Explosive Device Defeat Organization’s (JIEDDO) proposal solicitation process enables military and non-military organizations to request funding for the development of Counter-Improvised Explosive Device (C-IED) projects. Decision Analysis (DA) methodology serves as a tool to assist the decision maker (DM) in making an informed decision. This research applies Value Focused Thinking …

Creating Multi Objective Value Functions From Non-Independent Values, Christopher D. Richards

Theses and Dissertations

Decisions are made every day and by everyone. As these decisions become more important, involve higher costs and affect a broader group of stakeholders it becomes essential to establish a more rigorous strategy than simply intuition or "going with your gut". In the past several decades, the concept of Value Focused Thinking (VFT) has gained much acclaim in assisting Decision Makers (DMs) in this very effort. By identifying and organizing what a DM values VFT is able to decompose the original problem and create a mathematical model to score and rank alternatives to be chosen. But what if the decision …

Using Agent-Based Modeling To Evaluate Uas Behaviors In A Target-Rich Environment, Joseph A. Van Kuiken

Theses and Dissertations

The trade-off between accuracy and speed is a re-occurring dilemma in many facets of military performance evaluation. This is an especially important issue in the world of ISR. One of the most progressive areas of ISR capabilities has been the utilization of Unmanned Aircraft Systems (UAS). Many people believe that the future of UAS lies in smaller vehicles flying in swarms. We use the agent-based System Effectiveness and Analysis Simulation (SEAS) to create a simulation environment where different configurations of UAS vehicles can process targets and provide output that allows us to gain insight into the benefits and drawbacks of …

Group Comparison Of Eigenvalues And Eigenvectors Of Diffusion Tensors, Armin Schwartzman, Robert F. Dougherty, Jonathan E. Taylor

Harvard University Biostatistics Working Paper Series

No abstract provided.

Characterizing The Statistical Properties And Global Distribution Of Dansgaard-Oeschger Events, Andrea Michelle Thomas

Theses and Dissertations

Ice core records from Greenland have shown times of rapid warming during the most recent glacial period, called Dansgaard-Oeschger (D-O) events. D-O events are important to our understanding of both past climate systems and modern climate volatility. In this paper, we present new approaches for statistically evaluating the existence of cyclicity in D-O events and the possible lagged correlation between the Greenland and Antarctica temperature records. Specifically, we consider permutation testing and bootstrapping methodologies for assessing the cyclicity of D-O events and the correlation between the Greenland and Antarctica records. We find that there is not enough evidence to conclude …

Enhancing The Communication Competency Of Business Undergraduates: A Consumer Socialization Perspective, K. C. Gehrt, M. O'Brien, David Mease

Faculty Publications

Explaining how individuals acquire the necessary skills and knowledge to effectively participate in society is often accomplished through Socialization Theory. We investigate numerous socialization agents and their relationship with the communication competency of university business majors. Communication competency (reading, writing, and verbal) was measured via both a standardized skill test and self report. Exploratory analysis was conducted upon high and low communication competency groups that were identified via cluster analysis. Our findings generally indicate the most important socialization agents are via personal interactions whereas the least important socialization agents are influencing via primarily electronic or media-based methods.