Statistics and Probability Commons^™

Modeling Residential Foreclosures In Kent County, Kaitlyn Ratkowiak

Student Summer Scholars Manuscripts

Residential Foreclosures in Kent County have become commonplace in the past few years. In this project, we hope to analyze data on foreclosures since 2004 to learn more about the mounting crisis, with the hope that we can identify neighborhoods at risk of foreclosures and its associated consequences.

Mean Survival Time From Right Censored Data, Ming Zhong, Kenneth R. Hess

COBRA Preprint Series

A nonparametric estimate of the mean survival time can be obtained as the area under the Kaplan-Meier estimate of the survival curve. A common modification is to change the largest observation to a death time if it is censored. We conducted a simulation study to assess the behavior of this estimator of the mean survival time in the presence of right censoring.

We simulated data from seven distributions: exponential, normal, uniform, lognormal, gamma, log-logistic, and Weibull. This allowed us to compare the results of the estimates to the known true values and to quantify the bias and the variance. Our …

Analysis Of Transient Growth In Iterative Learning Control Using Pseudospectra, Douglas A. Bristow, John R. Singler

Mechanical and Aerospace Engineering Faculty Research & Creative Works

In this paper we examine the problem of transient growth in Iterative Learning Co ntrol (ILC). Transient growth is generally avoided in design by using robust monotonic convergence (RMC) criteria. However, RMC leads to fundamental performance limitations. We consider the possibility of allowing safe transient growth in ILC algorithms as a means to circumvent these limitations. Here the pseudospectra is used for the first time to study transient growth in ILC. Basic properties of the pseudospectra that are relevant to the ILC problem are presented. Two ILC design problems are considered and examined using pseduospectra. The pseudospectra provides new results …

Development And Implementation Of High-Throughput Snpgenotyping In Barley, Serdar Bozdag, Timothy J. Close, Prasanna R. Bhat, Stefano Lonardi, Yonghui Wu, Nils Rostoks, Luke Ramsay, Arnis Druka, Nils Stein, Jan T. Svensson, Steve Wanamaker, Mikeal L. Roose, Matthew J. Moscou, Shiaoman Chao, Rajeev K. Varshney, Peter Szucs, Kazuhiro Sato, Patrick M. Hayes, David E. Matthews, Andris Kleinhofs, Gary J. Muehlbauer, Joseph Deyoung, David F. Marshall, Kavitha Madishetty, Raymond D. Fenton, Pascal Condamine, Andreas Graner, Robbie Waugh

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

High density genetic maps of plants have, nearly without exception, made use of marker datasets containing missing or questionable genotype calls derived from a variety of genic and non-genic or anonymous markers, and been presented as a single linear order of genetic loci for each linkage group. The consequences of missing or erroneous data include falsely separated markers, expansion of cM distances and incorrect marker order. These imperfections are amplified in consensus maps and problematic when fine resolution is critical including comparative genome analyses and map-based cloning. Here we provide a new paradigm, a high-density consensus genetic map of …

An Adaptive Bayesian Approach To Dose-Response Modeling, Thomas J. Leininger

Theses and Dissertations

Clinical drug trials are costly and time-consuming. Bayesian methods alleviate the inefficiencies in the testing process while providing user-friendly probabilistic inference and predictions from the sampled posterior distributions, saving resources, time, and money. We propose a dynamic linear model to estimate the mean response at each dose level, borrowing strength across dose levels. Our model permits nonmonotonicity of the dose-response relationship, facilitating precise modeling of a wider array of dose-response relationships (including the possibility of toxicity). In addition, we incorporate an adaptive approach to the design of the clinical trial, which allows for interim decisions and assignment to doses based …

Approximating Stationary Statistical Properties, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. the main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. the result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are …

Random Walks With Elastic And Reflective Lower Boundaries, Lucas Clay Devore

Masters Theses & Specialist Projects

No abstract provided.

On The Testing And Estimation Of High-Dimensional Covariance Matrices, Thomas Fisher

All Dissertations

Many applications of modern science involve a large number of parameters. In
many cases, the number of parameters, p, exceeds the number of observations,
N. Classical multivariate statistics are based on the assumption that the
number of parameters is fixed and the number of observations is large. Many of
the classical techniques perform poorly, or are degenerate, in high-dimensional
situations.
In this work, we discuss and develop statistical methods for inference of
data in which the number of parameters exceeds the number of observations.
Specifically we look at the problems of hypothesis testing regarding and the
estimation of the covariance …

Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang

Mathematics Faculty Publications

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem

uu_xu_xxx 0 < x < 1, t > 0, (*)

It is shown …

The Development Of An Advanced Filial Therapy Model, Amy Cathleen Wickstrom

Loma Linda University Electronic Theses, Dissertations & Projects

This study sought to develop an advanced filial therapy model by examining the experiences of seven parents who participated in a preliminary advanced filial therapy intervention. These parents had previously completed a 10-week basic filial therapy model called Child Parent Relationship Therapy. A phenomenological qualitative design was employed, wherein data was obtained from parent playtime notes, researcher field notes, group process transcriptions, and focus groups. Parent experiences of the intervention were examined from a systems-relational lens, and four categories emerged, which include relational epiphanies, enhanced understanding of the playtimes, model format, and skill development. Additionally, a variety of themes were …

Using Labeled Data To Evaluate Change Detectors In A Multivariate Streaming Environment, Albert Y. Kim, Caren Marzban, Donald B. Percival, Werner Stuetzle

Statistical and Data Sciences: Faculty Publications

We consider the problem of detecting changes in a multivariate data stream. A change detector is defined by a detection algorithm and an alarm threshold. A detection algorithm maps the stream of input vectors into a univariate detection stream. The detector signals a change when the detection stream exceeds the chosen alarm threshold. We consider two aspects of the problem: (1) setting the alarm threshold and (2) measuring/comparing the performance of detection algorithms. We assume we are given a segment of the stream where changes of interest are marked. We present evidence that, without such marked training data, it might …

U.S. Chamber Of Commerce Liability Survey: Inaccurate, Unfair, And Bad For Business, Theodore Eisenberg

Cornell Law Faculty Publications

The U.S. Chamber of Commerce uses its Survey of State Liability to criticize judiciaries and seek legal change but no detailed evaluation of the survey’s quality exists. This article presents evidence that the survey is substantively inaccurate and methodologically flawed. It incorrectly characterizes state law; respondents provide less than 10 percent correct answers for objectively verifiable responses. It is internally inconsistent; a state threatened with judicial hellhole status ranked first in the survey while venues not on the list ranked lower. The absence of correlation between survey rankings and observable activity suggests that other factors drive the rankings. Two factors …

Fully Exponential Laplace Approximation Em Algorithm For Nonlinear Mixed Effects Models, Meijian Zhou

Department of Statistics: Dissertations, Theses, and Student Research

Nonlinear mixed effects models provide a flexible and powerful platform for the analysis of clustered data that arise in numerous fields, such as pharmacology, biology, agriculture, forestry, and economics. This dissertation focuses on fitting parametric nonlinear mixed effects models with single- and multi-level random effects. A new, efficient, and accurate method that gives an error of order O(1/n²), fully exponential Laplace approximation EM algorithm (FELA-EM), for obtaining restricted maximum likelihood (REML) estimates in nonlinear mixed effects models is developed. Sample codes for implementing FELA-EM algorithm in R are given. Simulation studies have been conducted to evaluate …

Optimal Filtering Of An Advertising Production System With Deteriorating Items, Lakhdar Aggoun, Ali Benmerzouga, Lotfi Tadj

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider an integrated stochastic advertising-production system in the case of a duopoly. Two firms spend certain amounts to advertise some product. The expenses processes evolve according to the jumps of two homogeneous, finite-state Markov chains. We assume that the items in stock may be subject to deterioration and the deterioration parameter is assumed to be random.

Risk Matrix Input Data Biases, Eric D. Smith, William T. Siefert, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Risk matrices used in industry characterize particular risks in terms of the likelihood of occurrence, and the consequence of the actualized risk. Human cognitive bias research led by Daniel Kahneman and Amos Tversky exposed systematic translations of objective probability and value as judged by human subjects. Applying these translations to the risk matrix allows the formation of statistical hypotheses of risk point placement biases. Industry-generated risk matrix data reveals evidence of biases in the judgment of likelihood and consequence-principally, likelihood centering, a systematic increase in consequence, and a diagonal bias. Statistical analyses are conducted with linear regression, normal distribution fitting, …

Statistical Analysis Of Linear Analog Circuits Using Gaussian Message Passing In Factor Graphs, Miti Phadnis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis introduces a novel application of factor graphs to the domain of analog circuits. It proposes a technique of leveraging factor graphs for performing statistical yield analysis of analog circuits that is much faster than the standard Monte Carlo/Simulation Program With Integrated Circuit Emphasis (SPICE) simulation techniques. We have designed a tool chain to model an analog circuit and its corresponding factor graph and then use a Gaussian message passing approach along the edges of the graph for yield calculation. The tool is also capable of estimating unknown parameters of the circuit given known output statistics through backward message …

A Practical Solution To The Reference Class Problem, Edward K. Cheng

Vanderbilt Law School Faculty Publications

The "reference class problem" is a serious challenge to the use of statistical evidence that arguably arises every day in wide variety of cases, including toxic torts, property valuation, and even drug smuggling. At its core, it observes that statistical inferences depend critically on how people, events, or things are classified. As there is (purportedly) no principle for privileging certain categories over others, statistics become manipulable, undermining the very objectivity and certainty that make statistical evidence valuable and attractive to legal actors. In this paper, I propose a practical solution to the reference class problem by drawing on model selection …

Metaevaluation Of Hiv/Aids Prevention Intervention Evaluations In Sub Saharan Africa With A Specific Emphasis On Implications For Women And Girls, Tererai Mafukidze Trent

Dissertations

Despite numerous attempts by international agencies to halt the spread of Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS), nowhere has the impact of HIV/AIDS been felt more acutely than among women and girls in Sub-Saharan Africa (SSA). SSA women account for 59% of adults over the age of 15 living with HIV/AIDS and 76% of those 15-24 who are infected (United Nations Joint Programme on HIV/AIDS [UNAIDS], 2007).

The evidence on gender disparities in infection rates is indisputable; there is an urgent need to identify what is missing in HIV/AIDS prevention interventions: What is the evidence based upon …

Kendall's Tau And Spearman's Rho For Zero-Inflated Data, Ronald Silva Pimentel

Dissertations

Zero-inflated continuous distributions have positive probability mass at zero in addition to a continuous distribution. Such type of data can be encountered, for example, in medical, environmental and financial research. The main focus of this research is to study the association of nonnegative random variables, both having a positive probability mass at zero. New estimators of the classical measures of association, Kendall's tau and Spearman's rho, appropriate for the zero-inflated distributions, are proposed and their asymptotic distributions are derived. Performance of the estimators is assessed by a Monte Carlo simulation study. New ideas are illustrated by a real data example.

A Two-Sample Adaptive Procedure Based On The Log-Rank And Peto And Peto's Wilcoxon Tests, Annie A. Tordilla

Dissertations

It has been shown that under a location-scale model y = μ + βz + σε at where y is right censored, the Log-Rank test is asymptotically efficient for the Extreme minimum value error distribution while Peto and Peto's Wilcoxon test is asymptotically efficient for the Logistic error distribution. We propose a two-sample adaptive test, which first selects between Extreme minimum value and Logistic error distribution as to which is a better fit to the data, then performs the asymptotically efficient test (Log-Rank or Peto and Peto's Wilcoxon test) for the selected distribution. The performance of the adaptive test is …

The Program Evaluation Standards Applied For Metaevaluation Purposes: Investigating Interrater Reliabiity And Implications For Use, Lori A. Wingate

Dissertations

Metaevaluation is the evaluation of evaluation. Metaevaluation may focus particular evaluation cases, evaluation systems, or the discipline overall. Leading scholars within the discipline consider metaevaluation to be a professional imperative, demonstrating that evaluation is a reflexive enterprise. Various criteria have been set forth for what constitutes excellence in evaluation. In the context of educational program evaluation, the dominant criteria are the Program Evaluation Standards, developed by the developed by the Joint Committee on Standards for Educational Evaluation.

There has been widespread acceptance and application of the Program Evaluation Standards, and their use is advocated by major organizations and several of …

Pragmatic Estimation Of A Spatio-Temporal Air Quality Model With Irregular Monitoring Data, Paul D. Sampson, Adam A. Szpiro, Lianne Sheppard, Johan Lindström, Joel D. Kaufman

UW Biostatistics Working Paper Series

Statistical analyses of the health effects of air pollution have increasingly used GIS-based covariates for prediction of ambient air quality in “land-use” regression models. More recently these regression models have accounted for spatial correlation structure in combining monitoring data with land-use covariates. The current paper builds on these concepts to address spatio-temporal prediction of ambient concentrations of particulate matter with aerodynamic diameter less than 2.5 μm (PM2.5) on the basis of a model representing spatially varying seasonal trends and spatial correlation structures. Our hierarchical methodology provides a pragmatic approach that fully exploits regulatory and other supplemental monitoring data which jointly …

On The Behaviour Of Marginal And Conditional Akaike Information Criteria In Linear Mixed Models, Sonja Greven, Thomas Kneib

Johns Hopkins University, Dept. of Biostatistics Working Papers

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive …

Survival Analysis With Error-Prone Time-Varying Covariates: A Risk Set Calibration Approach, Xiaomei Liao, David M. Zucker, Yi Li, Donna Spiegelman

Harvard University Biostatistics Working Paper Series

No abstract provided.

Is Survival The Only Or Even The Right Outcome For Evaluating Treatments For Out-Of-Hospital Cardiac Arrest? A Proposed Test Based On Both An Intermediate And Ultimate Outcome., Al Hallstrom

UW Biostatistics Working Paper Series

It is generally agreed that the goal of resuscitation is survival with neurological and physiological status similar to that preceding the cardiac arrest. Previously I have argued that the lack of improvement in outcome from resuscitation over the past 3 to 4 decades, as compared to the substantial progress made in treatment of ischemic heart disease, is a consequence of the absence of randomized clinical trials of new interventions and the use of intermediate endpoints such as return of spontaneous circulation or admittance to hospital. Proponents of these intermediate endpoints have argued that those involved in the resuscitation have no …

A New Class Of Minimum Power Divergence Estimators With Applications To Cancer Surveillance, Nirian Martin, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Nonlinear Models In Multivariate Population Bioequivalence Testing, Bassam Dahman

Theses and Dissertations

In this dissertation a methodology is proposed for simultaneously evaluating the population bioequivalence (PBE) of a generic drug to a pre-licensed drug, or the bioequivalence of two formulations of a drug using multiple correlated pharmacokinetic metrics. The univariate criterion that is accepted by the food and drug administration (FDA) for testing population bioequivalence is generalized. Very few approaches for testing multivariate extensions of PBE have appeared in the literature. One method uses the trace of the covariance matrix as a measure of total variability, and another uses a pooled variance instead of the reference variance. The former ignores the correlation …

Two-Stage Decompositions For The Analysis Of Functional Connectivity For Fmri With Application To Alzheimer's Disease Risk, Brian S. Caffo, Ciprian M. Crainiceanu, Guillermo Verduzco, Stewart H. Mostofsky, Susan Spear-Bassett, James J. Pekar

COBRA Preprint Series

Functional connectivity is the study of correlations in measured neurophysiological signals. Altered functional connectivity has been shown to be associated with numerous diseases including Alzheimer's disease and mild cognitive impairment. In this manuscript we use a two-stage application of the singular value decomposition to obtain data driven population-level measures of functional connectivity in functional magnetic resonance imaging (fMRI). The method is computationally simple and amenable to high dimensional fMRI data with large numbers of subjects. Simulation studies suggest the ability of the decomposition methods to recover population brain networks and their associated loadings. We further demonstrate the utility of these …

Parameter Estimation For The Lognormal Distribution, Brenda Faith Ginos

Theses and Dissertations

The lognormal distribution is useful in modeling continuous random variables which are greater than or equal to zero. Example scenarios in which the lognormal distribution is used include, among many others: in medicine, latent periods of infectious diseases; in environmental science, the distribution of particles, chemicals, and organisms in the environment; in linguistics, the number of letters per word and the number of words per sentence; and in economics, age of marriage, farm size, and income. The lognormal distribution is also useful in modeling data which would be considered normally distributed except for the fact that it may be more …

Analyzing Bivariate Survival Data With Interval Sampling And Application To Cancer Epidemiology, Hong Zhu, Mei-Cheng Wang

Johns Hopkins University, Dept. of Biostatistics Working Papers

In medical follow-up studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as the outcomes to identify the progression of a disease. In cancer studies interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme where the first failure event (cancer onset) is identified within a calendar time interval, the time of the initiating event (birth) can be retrospectively confirmed, and the occurrence of the second event (death) is observed sub ject to right censoring. To …