Physical Sciences and Mathematics Commons^™

Unit Rectangle Visibility Graphs, Alice M. Dean, Joanna A. Ellis-Monaghan, Sarah J. Hamilton, Greta Pangborn

Mathematics, Statistics and Computer Science Faculty Research and Publications

Over the past twenty years, rectangle visibility graphs have generated consider- able interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph G is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a non-degenerate …

Extending The Information Partition Function: Modeling Interaction Effects In Highly Multivariate, Discrete Data, Paul C. Cannon

Theses and Dissertations

Because of the huge amounts of data made available by the technology boom in the late twentieth century, new methods are required to turn data into usable information. Much of this data is categorical in nature, which makes estimation difficult in highly multivariate settings. In this thesis we review various multivariate statistical methods, discuss various statistical methods of natural language processing (NLP), and discuss a general class of models described by Erosheva (2002) called generalized mixed membership models. We then propose extensions of the information partition function (IPF) derived by Engler (2002), Oliphant (2003), and Tolley (2006) that will allow …

Model-Robust Bayesian Regression And The Sandwich Estimator, Adam A. Szpiro, Kenneth M. Rice, Thomas Lumley

UW Biostatistics Working Paper Series

PLEASE NOTE THAT AN UPDATED VERSION OF THIS RESEARCH IS AVAILABLE AS WORKING PAPER 338 IN THE UNIVERSITY OF WASHINGTON BIOSTATISTICS WORKING PAPER SERIES (http://www.bepress.com/uwbiostat/paper338).

In applied regression problems there is often sufficient data for accurate estimation, but standard parametric models do not accurately describe the source of the data, so associated uncertainty estimates are not reliable. We describe a simple Bayesian approach to inference in linear regression that recovers least-squares point estimates while providing correct uncertainty bounds by explicitly recognizing that standard modeling assumptions need not be valid. Our model-robust development parallels frequentist estimating equations and leads to intervals …

Spatio-Temporal Associations Between Goes Aerosol Optical Depth Retrievals And Ground-Level Pm2.5, Christopher J. Paciorek, Yang Liu, Hortensia Moreno-Macias, Shobha Kondragunta

Harvard University Biostatistics Working Paper Series

We assess the strength of association between aerosol optical depth (AOD) retrievals from the GOES Aerosol/Smoke Product (GASP) and ground-level fine particulate matter (PM2.5) to assess AOD as a proxy for PM2.5 in the United States. GASP AOD is retrieved from a geostationary platform and therefore provides dense temporal coverage with half-hourly observations every day, in contrast to once per day snapshots from polar-orbiting satellites. However, GASP AOD is based on a less-sophisticated instrument and retrieval algorithm. We find that correlations between GASP AOD and PM2.5 over time at fixed locations are reasonably high, except in the winter and in …

New Technique For Imputing Missing Item Responses For An Ordinal Variable: Using Tennessee Youth Risk Behavior Survey As An Example., Andaleeb Abrar Ahmed

Electronic Theses and Dissertations

Surveys ordinarily ask questions in an ordinal scale and often result in missing data. We suggest a regression based technique for imputing missing ordinal data. Multilevel cumulative logit model was used with an assumption that observed responses of certain key variables can serve as covariate in predicting missing item responses of an ordinal variable. Individual predicted probabilities at each response level were obtained. Average individual predicted probabilities for each response level were used to randomly impute the missing responses using a uniform distribution. Finally, likelihood ratio chi square statistics was used to compare the imputed and observed distributions. Two other …

Examining Significant Differences Of Gunshot Residue Patterns Using Same Make And Model Of Firearms In Forensic Distance Determination Tests., Heather Lewey

Electronic Theses and Dissertations

In many cases of crimes involving a firearm, police investigators need to know how far the firearm was held from the victim when it was discharged. Knowing this distance, vital questions regarding the re-construction of the crime scene can be known. Often, the original firearm used in commission of a suspected crime is not available for testing or is damaged. Crime laboratories require the original firearm in order to conduct distance determination tests. However, no empirical research has ever been conducted to determine if same make and model firearms produce different results in distance determination testing. It was the purpose …

Probability And Statistics For Third Through Fifth Grade Classrooms., Melissa Taylor Mckinnon

Electronic Theses and Dissertations

This document contains a variety of lesson plans that can be readily used by a teacher of intermediate students. This thesis contains two units in Probability and one unit in Statistics. Any educator can supplement this document with any curriculum to teach lessons from vocabulary to concept.

Self-Management Of Type 2 Diabetes In Appalachina Women., Melissa Joy Magness

Electronic Theses and Dissertations

Gender, minority, and regional-related disparities have been documented in diabetes management. Self-efficacy, the belief in one's ability to carry out the actions mandated by a task, has been identified as a key predictor in glycemic control; however, it has not been investigated in rural, female populations. This cross-sectional, correlation investigation examined the relationships among self-efficacy, depression, and diabetes self-care management in women living in Appalachia with type 2 diabetes. Using Bandura's Social Cognitive Theory, 85 women ages ≥ 21 with type 2 diabetes for a minimum of 6 months who were residents in Appalachia completed the 1) Diabetes Self-Efficacy Scale, …

Estimating Sensitivity And Specificity From A Phase 2 Biomarker Study That Allows For Early Termination, Margaret S. Pepe Phd

UW Biostatistics Working Paper Series

Development of a disease screening biomarker involves several phases. In phase 2 its sensitivity and specificity is compared with established thresholds for minimally acceptable performance. Since we anticipate that most candidate markers will not prove to be useful and availability of specimens and funding is limited, early termination of a study is appropriate if accumulating data indicate that the marker is inadequate. Yet, for markers that complete phase 2, we seek estimates of sensitivity and specificity to proceed with the design of subsequent phase 3 studies.

We suggest early stopping criteria and estimation procedures that adjust for bias caused by …

Systematic Reviews Of Animal Experiments Demonstrate Poor Human Clinical And Toxicological Utility, Andrew Knight

Experimentation Collection

The assumption that animal models are reasonably predictive of human outcomes provides the basis for their widespread use in toxicity testing and in biomedical research aimed at developing cures for human diseases. To investigate the validity of this assumption, the comprehensive Scopus biomedical bibliographic databases were searched for published systematic reviews of the human clinical or toxicological utility of animal experiments. In 20 reviews in which clinical utility was examined, the authors concluded that animal models were either significantly useful in contributing to the development of clinical interventions, or were substantially consistent with clinical outcomes, in only two cases, one …

Exact Confidence Bounds For The Risk Ratio In 2x2 Tables With Structural Zero, Chris J. Lloyd, Max Moldovan

Chris J. Lloyd

This paper examines exact one-sided confidence limits for the risk ratio in a 2x2 table with structural zero. Starting with four approximate lower and upper limits, we adjust each using the algorithm of Buehler (1957) to arrive at lower (upper) limits that have exact coverage properties and are as large (small) as possible subject to coverage, as well as an ordering, constraint. Different Buehler limits are compared by their mean size, since all are exact in their coverage. Buehler limits based on the signed root likelihood ratio statistic are found to have the best performance and recommended for practical use.

Statistical Issues In Proteomic Research, Jeffrey S. Morris

Jeffrey S. Morris

No abstract provided.

Bayesian Analysis For Penalized Spline Regression Using Win Bugs, Ciprian M. Crainiceanu, David Ruppert, M.P. Wand

Johns Hopkins University, Dept. of Biostatistics Working Papers

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. MCMC mixing is substantially improved from the previous versions by using low{rank thin{plate splines instead of truncated polynomial basis. Simulation time …

Statistics In The Jury Box: How Jurors Respond To Mitochondrial Dna Match Probabilities, David H. Kaye, Valerie P. Hans, B. Michael Dann, Erin J. Farley, Stephanie Albertson

Cornell Law Faculty Publications

This article describes parts of an unusually realistic experiment on the comprehension of expert testimony on mitochondrial DNA (mtDNA) sequencing in a criminal trial for robbery. Specifically, we examine how jurors who responded to summonses for jury duty evaluated portions of videotaped testimony involving probabilities and statistics. Although some jurors showed susceptibility to classic fallacies in interpreting conditional probabilities, the jurors as a whole were not overwhelmed by a 99.98% exclusion probability that the prosecution presented. Cognitive errors favoring the defense were more prevalent than ones favoring the prosecution. These findings lend scant support to the legal argument that mtDNA …

The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …

On The Total Duration Of Negative Surplus Of A Risk Process With Two-Step Premium Function, Pavlina Jordanova

Applications and Applied Mathematics: An International Journal (AAM)

We consider a risk reserve process whose premium rate reduces from c_d to c_u when the reserve comes above some critical value v. In the model of Cramer-Lundberg with initial capital u ≥ 0, we obtain the probability that ruin does not occur before the first up-crossing of level v. When u < v, following H. Gerber and E. Shiu (1997), we derive the probability that starting with initial capital u ruin occurs and the severity of ruin is not bigger than v. Further we express the probability of ruin in the two step premium function model - ψ (u,v), by the last two probabilities. Our assumptions imply that the surplus process will go to infinity almost surely. This entails that the process will stay below zero only temporarily. We derive the distribution of the total duration of negative surplus and obtain its Laplace transform and mean value. As a consequence of these results, under certain conditions in the Model of Cramer-Lundberg we obtain the expected value of the severity of ruin. In the end of the paper we give examples with exponential claim sizes.

A Study Of The Relationship Between American Evangelicals And Human Rights, Amy Rachel Timmons Stumpf

Loma Linda University Electronic Theses, Dissertations & Projects

Human rights violations and abuses affect every region of the globe. The most recent Amnesty International Annual Report details violations in 149 countries. While there are no simple solutions to a problem of this magnitude and complexity, the support of powerful social groups can help in providing relief to the victims, pressure on abusive governments, legal consequences for abusers, and other resources in combating the violence that seems to chronically plague over our world. One of the most powerful groups, with tremendous social capital, is American evangelicals. Evangelicalism, even given the loose and informal organizational structures, is one of the …

Immediate Implant Placement In Extraction Sites With Periapical Lesions: A Retrospective Study, Yuan-Lung Hung

Loma Linda University Electronic Theses, Dissertations & Projects

Immediate implant placement into fresh extraction sites has become a relatively routine clinical procedure with a favorable prognosis. However, immediate placement into extraction sockets with lesions has not been extensively documented in humans. Therefore, the purpose of this study was to retrospectively determine the survival rate of implants placed into extraction sockets with visible periapical lesions.

Patient charts of 544 immediately placed implants from Loma Linda University School of Dentistry, Center for Prosthodontics and Implant Dentistry were examined. Eighty-six of the 544 implants had been placed immediately into extraction sockets with periapical lesions and they were included in this study. …

Efficacy Of Cognitive Therapy And Pharmacotherapy In Depression: A Meta-Analysis, Daniel B. Michel

Loma Linda University Electronic Theses, Dissertations & Projects

A meta-analysis comparing the long-term effectiveness of cognitive behavioral therapy (CBT) and pharmacotherapy in preventing relapse following treatment discontinuation was performed using published studies of depressed participants. Twenty-three articles met inclusionary criteria and were included in the analyses. Weighted effect sizes and moderators, treatment type, were calculated using statistical analysis software. Initially, fixed effects models were applied to the data, but due to significant between-group heterogeneity that could not be fully explained by treatment type, mixed effect models were used to account for the residual heterogeneity. Results indicated that overall, depressed individuals treated to remission with CBT evidence decreased relapse …

Diagnostics For Choosing Between Log-Rank And Wilcoxon Tests, Ruvie Lou Maria Custodio Martinez

Dissertations

Two commonly used tests for comparison of survival curves are the generalized Wilcoxon procedure of Gehan (1965) and Breslow (1970) and the Log-rank test proposed by Mantel (1966) and Cox (1972). In applications, the Log-rank test is used after checking for validity of the proportional hazards (PH) assumption, with Wilcoxon being the fallback method when the PH assumption fails.

However, the relative performance of the two procedures depend not just on the PH assumption but also on the pattern of differences between the two curves. We will show that the crucial factor is whether the differences tend to occur early …

Extensions Of Two-Part Tests To Compare K Independent Populations, Marwan Daoud

Dissertations

We consider two-part models that are mixtures of a point-mass variable with all mass at zero and a continuous random variable. The model may assume a particular distributionh(x) for the continuous part such as a log-normal or a gamma. The response variable is defined as y=(x, d), where d=1 if x > 0 and d=0 if x = 0. The probability distribution function has the following form: fx,d=p ^1-d×1-p ×hx ^d.

Lachenbruch (1976, 2001) proposed several tests to compare means of two populations for this type of data. We proposed a two-part Wald test and …

Exact One-Sided Confidence Limits For The Difference Between Two Correlated Proportions, Chris Lloyd, Max V. Moldovan

Chris J. Lloyd

We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler (1957). Starting with five different approximate loer and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.

Trends In Uspto Office Actions, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

Clustering Methods For Delineating Regions Of Spatial Stationarity, Jared M. Collings

Theses and Dissertations

This paper seeks to further investigate data extracted by the use of Functional Magnetic Resonance Imaging (FMRI) as it is applied to brain tissue and how it measures blood flow to certain areas of the brain following the application of a stimulus. As a precursor to detailed spatial analysis of this kind of data, this paper develops methods of grouping data based on the necessary conditions for spatial statistical analysis. The purpose of this paper is to examine and develop methods that can be used to delineate regions of stationarity. One of the major assumptions used in spatial estimation is …

Modeling Transition Probabilities For Loan States Using A Bayesian Hierarchical Model, Rebecca Lee Monson

Theses and Dissertations

A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can …

Longitudinal Data With Follow-Up Truncated By Death: Finding A Match Between Analysis Method And Research Aims, Brenda Kurland, Laura Lee Johnson, Paula Diehr

UW Biostatistics Working Paper Series

Diverse analysis approaches have been proposed to distinguish data missing due to death from nonresponse, and to summarize trajectories of longitudinal data truncated by death. We demonstrate how these analysis approaches arise from factorizations of the distribution of longitudinal data and survival information. Models are illustrated using hypothetical data examples (cognitive functioning in older adults, and quality of life under hospice care) and up to 10 annual assessments of longitudinal cognitive functioning data for 3814 participants in an observational study. For unconditional models, deaths do not occur, deaths are independent of the longitudinal response, or the unconditional longitudinal response averages …

Correction: Using Participatory Design To Develop (Public) Health Decision Support Systems Through Gis, S. Michelle Driedger, Anita Kothari, Jason Morrison, Michael Sawada, Eric J. Crighton, Ian D. Graham

Anita Kothari

Background: Organizations that collect substantial data for decision-making purposes are often characterized as being 'data rich' but 'information poor'. Maps and mapping tools can be very useful for research transfer in converting locally collected data into information. Challenges involved in incorporating GIS applications into the decision-making process within the non-profit (public) health sector include a lack of financial resources for software acquisition and training for nonspecialists to use such tools. This on-going project has two primary phases. This paper critically reflects on Phase 1: the participatory design (PD) process of developing a collaborative web-based GIS tool.

Methods: A case study …

Decomposition Of Regression Estimators To Explore The Influence Of "Unmeasured" Time-Varying Confounders, Yun Lu, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth …

Weight, Mortality, Years Of Healthy Life, And Active Life Expectancy In Older Adults, Paula Diehr

Paula Diehr

OBJECTIVES: To determine whether weight categories predict subsequent mortality and morbidity in older adults. DESIGN: Multistate life tables, using data from the Cardiovascular Health Study, a longitudinal population-based cohort of older adults. SETTING: Data were provided by community-dwelling seniors in four U.S. counties: Forsyth County, North Carolina; Sacramento County, California; Washington County, Maryland; and Allegheny County, Pennsylvania. PARTICIPANTS: Five thousand eight hundred eighty-eight adults aged 65 and older at baseline. MEASUREMENTS: The age- and sex-specific probabilities of transition from one health state to another and from one weight category to another were estimated. From these probabilities, future life expectancy, years …

A Parametric Roc Model Based Approach For Evaluating The Predictiveness Of Continuous Markers In Case-Control Studies, Ying Huang, Margaret Pepe

UW Biostatistics Working Paper Series

The predictiveness curve shows the population distribution of risk endowed by a marker or risk prediction model. It provides a means for assessing the model's capacity for risk stratification. Methods for making inference about the predictiveness curve have been developed using cross-sectional or cohort data. Here we consider inference based on case-control studies and prior knowledge about prevalence or incidence of the outcome. We exploit the relationship between the ROC curve and the predictiveness curve given disease prevalence. Methods are developed for deriving the predictiveness curve from a parametric ROC model. Estimation of the whole range and of a portion …