Statistics and Probability Commons^™

A Computational Method For Estimating And Finding The Hconfidence Interval Of The Ratio Scale Parameters In The Two-Sample Problem, Mona Abdullah Alduailij

Dissertations

Testing equality of variances between two samples is applied in various fields. However, in the absence of non-normal assumptions, equality of variance tests would not yield robust results. In real life situation, the absence of such assumptions is even evident, which calls for more reliable tests to accommodate for the lack of these assumptions. There are abundant parametric and nonparametric methods for estimating the scale parameter; yet a distribution-free method for estimating and finding the confident interval ratio of scale parameters in the two-sample problem would be a reliable alternative. A comparison between existing parametric and non-parametric rank tests for …

A Data Generating Review That Bops, Twists And Pulls At Misconceptions, Kimberly Gardner

Faculty Articles

Statistics is an integral part of the K-12 mathematics curriculum (age 5-18). Naturally, students construct misconceptions of what they learn. This article discusses The Bop It^© Challenge, a review activity assesses student understanding and reveals their misundertandings of statistical concepts.

A Comparative Study Of Exact Versus Propensity Matching Techniques Using Monte Carlo Simulation, Mukaria J. J. Itang'ata

Dissertations

Often researchers face situations where comparative studies between two or more programs are necessary to make causal inferences for informed policy decision-making. Experimental designs employing randomization provide the strongest evidence for causal inferences. However, many pragmatic and ethical challenges may preclude the use of randomized designs. In such situations, subject matching provides an alternative design approach for conducting causal inference studies. This study examined various design conditions hypothesized to affect matching procedures’ bias recovery ability.

See attachment for full abstract.

Daily Walking And Life Expectancy Of Elderly People In The Iowa 65+ Rural Health Study, Hani M. Samawi

Biostatistics: Faculty Publications

The purpose of this paper is to investigate the hypothesis that outdoor daily walking, as an exercise, has an effect on the rate of mortality among those elderly people in the Iowa 65+ Rural Health Study (RHS). RHS is a prospective longitudinal cohort study of 8 years follow-up from 1981 to 1989. It consists of a random sample of 3,673 individuals (1,420 men and 2,253 women) aged 65 or older living in Washington and Iowa counties of the State of Iowa. Our analysis was conducted only on those non-institutional individuals who could without any help walk across a small room; …

Analysis Of Continuous Longitudinal Data With Arma(1, 1) And Antedependence Correlation Structures, Sirisha Mushti

Mathematics & Statistics Theses & Dissertations

Longitudinal or repeated measure data are common in biomedical and clinical trials. These data are often collected on individuals at scheduled times resulting in dependent responses. Inference methods for studying the behavior of responses over time as well as methods to study the association with certain risk factors or covariates taking into account the dependencies are of great importance. In this research we focus our study on the analysis of continuous longitudinal data. To model the dependencies of the responses over time, we consider appropriate correlation structures generated by the stationary and non-stationary time-series models. We develop new estimation procedures …

Characterization Of A Weighted Quantile Score Approach For Highly Correlated Data In Risk Analysis Scenarios, Caroline Carrico

Theses and Dissertations

In risk evaluation, the effect of mixtures of environmental chemicals on a common adverse outcome is of interest. However, due to the high dimensionality and inherent correlations among chemicals that occur together, the traditional methods (e.g. ordinary or logistic regression) are unsuitable. We extend and characterize a weighted quantile score (WQS) approach to estimating an index for a set of highly correlated components. In the case with environmental chemicals, we use the WQS to identify “bad actors” and estimate body burden. The accuracy of the WQS was evaluated through extensive simulation studies in terms of validity (ability of the WQS …

Some New Applications Of P-P Plots, Isha Dewan, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

The P-P plot is a powerful graphical tool to compare stochastically the magnitudes of two random variables. In this note, we introduce a new partial order, called P?P order based on P-P plots. For a pair of random variables (X ₁, Y₁) and (X ₂, Y ₂) one can see the relative precedence of Y ₂ over X ₂ versus that of Y ₁ over X ₁ using P-P order. We show that several seemingly very technical and difficult concepts like convex transform order and super-additive ordering can be easily explained with the …

Oscillation Of Third-Order Nonlinear Delay Differential Equations, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we study the oscillatory behavior of a class of third-order nonlinear delay differential equations (a(t)(b(t)y′(t)) ′) ′+q(t)yγ(τ(t)) =0. Some new oscillation criteria are presented by transforming this equation to the first order delayed and advanced differential equations. Employing suitable comparison theorems, we establish new results on oscillation of the studied equation. Assumptions in our theorems are less restrictive; these criteria improve those in the recent paper [Appl. Math. Comput., 202 (2008), 102-112] and related contributions to the subject. Examples are provided to illustrate new results.

Vertically Shifted Mixture Models For Clustering Longitudinal Data By Shape, Brianna C. Heggeseth, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

Longitudinal studies play a prominent role in health, social and behavioral sciences as well as in the biological sciences, economics, and marketing. By following subjects over time, temporal changes in an outcome of interest can be directly observed and studied. An important question concerns the existence of distinct trajectory patterns. One way to determine these distinct patterns is through cluster analysis, which seeks to separate objects (subjects, patients, observational units) into homogeneous groups. Many methods have been adapted for longitudinal data, but almost all of them fail to explicitly group trajectories according to distinct pattern shapes. To fulfill the need …

Efficient Estimation Of Risk Ratios From Clustered Binary Data, Matthew Cefalu, Eric Tchetgen Tchetgen

Harvard University Biostatistics Working Paper Series

No abstract provided.

Causes Of Death In Surgically Treated Patients With Type A Aortic Dissection - A Ten Year Review, James K. Wu Md, Eilizabeth Depaolo Bs, Theodore G. Phillips Md, Timothy S. Misselbeck

Department of Surgery

No abstract provided.

Extensions For The Epsilon Skew Exponential Power Distribution Family, Ahmad N. Flaih

Theses and Dissertations

Practical applied statistics reveals that the analysis of many real data that exhibit both fat-tailless and skewness shows significant departures from normality assumptions. In these circumstances, the adoption of more flexible models that cope with near normal data may be appropriate in place of adopting the robust approach, semi-parametric or nonparametric models, and Box-Cox transformation. An alternative approach is to consider using the Epsilon Skew Exponential Power (ESEP) distribution developed by Elsalloukh [12] and [15] which embeds the normal, fat-tailedness, and skewness distributions as special cases. We develop models based on using the ESEP family, in particular, the ESEP receiver …

The Net Reclassification Index (Nri): A Misleading Measure Of Prediction Improvement With Miscalibrated Or Overfit Models, Margaret Pepe, Jin Fang, Ziding Feng, Thomas Gerds, Jorgen Hilden

UW Biostatistics Working Paper Series

The Net Reclassification Index (NRI) is a very popular measure for evaluating the improvement in prediction performance gained by adding a marker to a set of baseline predictors. However, the statistical properties of this novel measure have not been explored in depth. We demonstrate the alarming result that the NRI statistic calculated on a large test dataset using risk models derived from a training set is likely to be positive even when the new marker has no predictive information. A related theoretical example is provided in which a miscalibrated risk model that includes an uninformative marker is proven to erroneously …

Simulation Insights Using R, Boyan Kostadinov

Publications and Research

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software R for Statistical Computing. The author illustrates the computer simulation approach by focusing on several problems of increasing difficulty. The simulation techniques and the specific problems discussed in this article would be of interest to STEM students and instructors, teaching courses in Monte Carlo simulations, stochastic modeling, probability and statistics. The R code for all problems is discussed in full detail so that the reader can get a taste of …

Predicting Human Movement Type Based On Multiple Accelerometers Using Movelets, Bing He, Jiawei Bai, Annemarie Koster, Casserotti Paolo, Nancy Glynn, Tamara B. Harris, Ciprian Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

We introduce statistical methods for prediction of types of human movement based on three tri-axial accelerometers worn simultaneously at the hip, left, and right wrist. We compare the individual performance of the three accelerometers using movelets and propose a new prediction algorithm that integrates the information from all three accelerometers. The development is motivated by a study of 20 older subjects who were instructed to perform 15 different types of activities during in-laboratory sessions. The differences in the prediction performance for different activity types among the three accelerometers reveal subtle yet important insights into how the intrinsic physical features of …

Journal Acceptance Policies On Etds, Chelsea Kern

Statistics

No abstract provided.

Is Obesity Socially Contagious?, Ciani Jean Sparks

Statistics

The main objective of this paper is to analyze three different articles that discuss whether obesity could be socially contagious. According to the World Health Organization in 2013, obesity is the fifth leading risk for deaths around the world. This disease has dramatically increased in the last decade, which has led scientists to believe there are other factors contributing to the epidemic besides genetics. The first article I analyzed, written by Nicholas Christakis and James Fowler, provided a logistic regression model to estimate the odds of a person becoming obese. The model included the explanatory variables: age, sex, education, smoking …

Immersed Finite Element Methods For Parabolic Equations With Moving Interface, Xiaoming He, Tao Lin, Yanping Lin, Xu Zhang

Mathematics and Statistics Faculty Research & Creative Works

This article presents three Crank-Nicolson-type immersed finite element (IFE) methods for solving parabolic equations whose diffusion coefficient is discontinuous across a time dependent interface. These methods can use a fixed mesh because IFEs can handle interface jump conditions without requiring the mesh to be aligned with the interface. These methods will be compared analytically in the sense of accuracy and computational cost. Numerical examples are provided to demonstrate features of these three IFE methods. © 2012 Wiley Periodicals, Inc.

Properties Of Higher-Order Half-Linear Functional Differential Equations With Noncanonical Operators, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

Some new results are presented for the oscillatory and asymptotic behavior of higher-order half-linear differential equations with a noncanonical operator. We study the delayed and advanced equations subject to various conditions. © 2013 Zhang et al.

Views On Sexual Assault Among Ifc Fraternities, Steven Legore

Statistics

The data collection and analysis for this project was performed for a consulting client Cierra, a fourth year Sociology major that works at the Safer Office on campus. She went to the consulting center on campus for help with the analysis of her project. She wanted to survey the IFC fraternities at Cal Poly on their views on sexual assault and rape. Thirteen IFC fraternities were surveyed with a total of 488 respondents. The responses to the 30 question True/False survey were used to evaluate the respondent’s empathy towards women, hostility towards women, and sexual aggression. Another research interest was …

A Bayesian Regression Tree Approach To Identify The Effect Of Nanoparticles Properties On Toxicity Profiles, Cecile Low-Kam, Haiyuan Zhang, Zhaoxia Ji, Tian Xia, Jeffrey I. Zinc, Andre Nel, Donatello Telesca

COBRA Preprint Series

We introduce a Bayesian multiple regression tree model to characterize relationships between physico-chemical properties of nanoparticles and their in-vitro toxicity over multiple doses and times of exposure. Unlike conventional models that rely on data summaries, our model solves the low sample size issue and avoids arbitrary loss of information by combining all measurements from a general exposure experiment across doses, times of exposure, and replicates. The proposed technique integrates Bayesian trees for modeling threshold effects and interactions, and penalized B-splines for dose and time-response surfaces smoothing. The resulting posterior distribution is sampled via a Markov Chain Monte Carlo algorithm. This …

A Graph-Theoretical Approach To The Selection Of The Minimum Tiling Path From A Physical Map, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of computing the minimum tiling path (MTP) from a set of clones arranged in a physical map is a cornerstone of hierarchical (clone-by-clone) genome sequencing projects. We formulate this problem in a graph theoretical framework, and then solve by a combination of minimum hitting set and minimum spanning tree algorithms. The tool implementing this strategy, called FMTP, shows improved performance compared to the widely used software FPC. When we execute FMTP and FPC on the same physical map, the MTP produced by FMTP covers a higher portion of the genome, and uses a smaller number of clones. For …

Rattus Model Utilizing Selective Pulmonary Ischemia Induces Bronchiolitis Obliterans Organizing Pneumonia, John C. Densmore, Paul M. Jeziorczak, Anne V. Clough, Kirkwood A. Pritchard Jr, Breana Cummens, Meetha Medhora, Arjun Rao, Elizabeth R. Jacobs

Mathematics, Statistics and Computer Science Faculty Research and Publications

Bronchiolitis obliterans organizing pneumonia (BOOP), a morbid condition when associated with lung transplant and chronic lung disease, is believed to be a complication of ischemia. Our goal was to develop a simple and reliable model of lung ischemia in the Sprague-Dawley rat that would produce BOOP. Unilateral ischemia without airway occlusion was produced by an occlusive slipknot placed around the left main pulmonary artery. Studies were performed 7 days later. Relative pulmonary and systemic flow to each lung was measured by injection of technetium Tc 99m macroaggregated albumin. Histological sections were examined for structure and necrosis and scored for BOOP. …

New Tools For Quantitative Decision Analysis In Applied Ecology And Conservation, Adam W. Schapaugh

School of Natural Resources: Dissertations, Theses, and Student Research

Scientists have generated a massive body of theory aimed at predicting and managing the impacts of anthropogenic activities on populations, species, and ecosystems. Transforming this research into knowledge that informs complex decision-making problems remains a major challenge in environmental management and conservation. My dissertation research aims to address this issue through the development and application of mathematical and statistical models. I integrate tools, concepts, and techniques from ecology, applied mathematics, computer science, and statistics to build structured decision-making frameworks for spatial prioritization, resource allocation, and optimal scheduling. I also tackle several of the technical challenges limiting the utility of such …

Design, Implications And Analysis Of Household Survey: Practical Issues To Note, O. O. Akanji

Bullion

This paper is to enhance the analytic processes of survey data as generated in the established household survey framework for economic policy management and decision making. The paper is divided into four sections. Section 1 is the introduction while Section 2 is the descriptive statistics emphasizing the models that bring out the relationship between the survey variables, Section 4 concludes and proffers recommendations.

Mind The Gaps, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Assessing The Impact Of Differential Genotyping Errors On Rare Variant Tests Of Association, Morgan Mayer-Jochimsen, Shannon Fast, Nathan L. Tintle

Faculty Work Comprehensive List

Genotyping errors are well-known to impact the power and type I error rate in single marker tests of association. Genotyping errors that happen according to the same process in cases and controls are known as non-differential genotyping errors, whereas genotyping errors that occur with different processes in the cases and controls are known as differential genotype errors. For single marker tests, non-differential genotyping errors reduce power, while differential genotyping errors increase the type I error rate. However, little is known about the behavior of the new generation of rare variant tests of association in the presence of genotyping errors. In …

Asymptotic And Finite Sample Behavior Of Net Reclassification Indices, Zheyu Wang

UW Biostatistics Working Paper Series

The Net Reclassification Index (NRI) introduced by Pencina and colleagues [1, 2] is designed to quantify the prediction increment provided by a new biomarker. It has become popular for evaluating and selecting novel markers. The published variance formulae for NRI statistics do not account for the fact that risks are estimated based on risk models fit to data, and thus are not valid in practice when estimated risks are used [3]. Kerr and colleagues [4] showed that the confidence intervals constructed based on a bootstrap estimate of the variance and Normal approximation had the best performance among various methods they …

On The Restricted Mean Event Time In Survival Analysis, Lu Tian, Lihui Zhao, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Surrogacy Assessment Using Principal Stratification When Surrogate And Outcome Measures Are Multivariate Normal, Anna Conlon, Jeremy M.G. Taylor, Michael R. Elliott

The University of Michigan Department of Biostatistics Working Paper Series

No abstract provided.