Statistics and Probability Commons^™

Section Abstracts: Statistics

Virginia Journal of Science

Abstracts of the Statistics Section for the 88th Annual Meeting of the Virginia Academy of Science, May 20-21, 2010, James Madison University, Harrisonburg, Virginia.

On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang

Mathematics and Statistics Faculty Publications

For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …

Insights Into The Commons On Flickr, Jason Vaughan

Library Faculty Research

The Commons on Flickr, comprised of an international community of select libraries, museums, and archives, was a project initially launched in 2008 by the Library of Congress and Flickr. Primary goals of The Commons are to broaden exposure to rich cultural heritage photographs and to observe and participate in the communities of engagement and dialog enabled through The Commons. A survey was administered to all The Commons institutions during summer 2009, focusing on assessment of the overall satisfaction of current members and seeking additional details on participation goals, social interactions, staff time involvement, and general statistics. Members report a very …

Knowing When To Say When: An Expanded Description Of Stopping Problems And Their Solutions, Eric C. Bauer

Mathematics

No abstract provided.

Efficient Design And Inference For Multi-Stage Randomized Trials Of Individualized Treatment Policies, Ree Dawson, Philip W. Lavori

COBRA Preprint Series

Increased clinical interest in individualized ‘adaptive’ treatment policies has shifted the methodological focus for their development from the analysis of naturalistically observed strategies to experimental evaluation of a pre-selected set of strategies via multi-stage designs. Because multi-stage studies often avoid the ‘curse of dimensionality’ inherent in uncontrolled studies, and hence the need to parametrically smooth trial data, it is not surprising in this context to find direct connections among different methodological approaches. We show by asymptotic and algebraic proof that the maximum likelihood (ML) and optimal semi-parametric estimators of the mean of a treatment policy and its standard error are …

Importance Sampling For Dispersion-Managed Solitons, Elaine T. Spiller, Gino Biondini

Mathematics, Statistics and Computer Science Faculty Research and Publications

The dispersion-managed nonlinear Schrödinger (DMNLS) equation governs the long-term dynamics of systems which are subject to large and rapid dispersion variations. We present a method to study large, noise-induced amplitude and phase perturbations of dispersion-managed solitons. The method is based on the use of importance sampling to bias Monte Carlo simulations toward regions of state space where rare events of interest—large phase or amplitude variations—are most likely to occur. Implementing the method thus involves solving two separate problems: finding the most likely noise realizations that produce a small change in the soliton parameters, and finding the most likely way that …

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Simple Examples Of Estimating Causal Effects Using Targeted Maximum Likelihood Estimation, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We present a brief overview of targeted maximum likelihood for estimating the causal effect of a single time point treatment and of a two time point treatment. We focus on simple examples demonstrating how to apply the methodology developed in (van der Laan and Rubin, 2006; Moore and van der Laan, 2007; van der Laan, 2010a,b). We include R code for the single time point case.

Can Animal Models Of Disease Reliably Inform Human Studies?, H. Bart Van Der Worp, David W. Howells, Emily Sena, Michelle J. Porritt, Sarah Rewell, Victoria O'Collins, Malcolm Macleod

Validation of Animal Experimentation Collection

• The value of animal experiments for predicting the effectiveness of treatment strategies in clinical trials has remained controversial, mainly because of a recurrent failure of interventions apparently promising in animal models to translate to the clinic.
• Translational failure may be explained in part by methodological flaws in animal studies, leading to systematic bias and thereby to inadequate data and incorrect conclusions about efficacy.
• Failures also result because of critical disparities, usually disease specific, between the animal models and the clinical trials testing the treatment strategy.
• Systematic review and meta-analysis of animal studies may aid in the selection of the most …

Publication Bias In Reports Of Animal Stroke Studies Leads To Major Overstatement Of Efficacy, Emily Sena, H. Bart Van Der Worp, Philip M.W. Bath, David W. Howells, Malcolm Macleod

Validation of Animal Experimentation Collection

The consolidation of scientific knowledge proceeds through the interpretation and then distillation of data presented in research reports, first in review articles and then in textbooks and undergraduate courses, until truths become accepted as such both amongst “experts” and in the public understanding. Where data are collected but remain unpublished, they cannot contribute to this distillation of knowledge. If these unpublished data differ substantially from published work, conclusions may not reflect adequately the underlying biological effects being described. The existence and any impact of such “publication bias” in the laboratory sciences have not been described. Using the CAMARADES (Collaborative Approach …

An Analysis Of Nonignorable Nonresponse In A Survey With A Rotating Panel Design, Caterina Giusti, Roderick J. Little

The University of Michigan Department of Biostatistics Working Paper Series

Missing values to income questions are common in survey data. When the probabilities of nonresponse are assumed to depend on the observed information and not on the underlining unobserved amounts, the missing income values are missing at random (MAR), and methods such as sequential multiple imputation can be applied. However, the MAR assumption is often considered questionable in this context, since missingness of income is thought to be related to the value of income itself, after conditioning on available covariates. In this article we describe a sensitivity analysis based on a pattern-mixture model for deviations from MAR, in the context …

Statistical Learning And Behrens-Fisher Distribution Methods For Heteroscedastic Data In Microarray Analysis, Nabin K. Manandhr-Shrestha

USF Tampa Graduate Theses and Dissertations

The aim of the present study is to identify the di®erentially expressed genes be- tween two di®erent conditions and apply it in predicting the class of new samples using the microarray data. Microarray data analysis poses many challenges to the statis- ticians because of its high dimensionality and small sample size, dubbed as "small n large p problem". Microarray data has been extensively studied by many statisticians and geneticists. Generally, it is said to follow a normal distribution with equal vari- ances in two conditions, but it is not true in general. Since the number of replications is very small, …

Panel Count Data Regression With Informative Observation Times, Petra Buzkova

UW Biostatistics Working Paper Series

When patients are monitored for potentially recurrent events such as infections or tumor metastases, it is common for clinicians to ask patients to come back sooner for follow-up based on the results of the most recent exam. This means that subjects’ observation times will be irregular and related to subject-specific factors. Previously proposed methods for handling such panel count data assume that the dependence between the events process and the observation time process is time-invariant. This article considers situations where the observation times are predicted by time-varying factors, such as the outcome observed at the last visit or cumulative exposure. …

Extensions Of Nearest Shrunken Centroid Method For Classification, Tomohiko Funai

Theses and Dissertations

Stylometry assumes that the essence of the individual style of an author can be captured using a number of quantitative criteria, such as the relative frequencies of noncontextual words (e.g., or, the, and, etc.). Several statistical methodologies have been developed for authorship analysis. Jockers et al. (2009) utilize Nearest Shrunken Centroid (NSC) classification, a promising classification methodology in DNA microarray analysis for authorship analysis of the Book of Mormon. Schaalje et al. (2010) develop an extended NSC classification to remedy the problem of a missing author. Dabney (2005) and Koppel et al. (2009) suggest other modifications of NSC. This paper …

Likelihood Ratio Testing For Admixture Models With Application To Genetic Linkage Analysis, Chong-Zhi Di, Kung-Yee Liang

Johns Hopkins University, Dept. of Biostatistics Working Papers

We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a special case of two component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. It has been widely used in genetic linkage analysis under heterogeneity, in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard and the LRT statistic does not converge to a conventional 2 distribution. In this paper, we investigate the asymptotic behavior of the LRT for …

Augmenting Latent Dirichlet Allocation And Rank Threshold Detection With Ontologies, Laura A. Isaly

Theses and Dissertations

In an ever-increasing data rich environment, actionable information must be extracted, filtered, and correlated from massive amounts of disparate often free text sources. The usefulness of the retrieved information depends on how we accomplish these steps and present the most relevant information to the analyst. One method for extracting information from free text is Latent Dirichlet Allocation (LDA), a document categorization technique to classify documents into cohesive topics. Although LDA accounts for some implicit relationships such as synonymy (same meaning) it often ignores other semantic relationships such as polysemy (different meanings), hyponym (subordinate), meronym (part of), and troponomys (manner). To …

Poverty, Vulnerability, And Provision Of Healthcare In Afghanistan, Jean-Francois Trani, Parul Bakhshi, Ayan A. Noor, Dominque Lopez, Ashraf Mashkoor

Brown School Faculty Publications

This paper presents findings on conditions of healthcare delivery in Afghanistan. There is an ongoing debate about barriers to healthcare in low-income as well as fragile states. In 2002, the Government of Afghanistan established a Basic Package of Health Services (BPHS), contracting primary healthcare delivery to non-state providers. The priority was to give access to the most vulnerable groups: women, children, disabled persons, and the poorest households. In 2005, we conducted a nationwide survey, and using a logistic regression model, investigated provider choice. We also measured associations between perceived availability and usefulness of healthcare providers. Our results indicate that the …

Parameter Estimation And Hypothesis Testing For The Truncated Normal Distribution With Applications To Introductory Statistics Grades, James T. Hattaway

Theses and Dissertations

The normal distribution is a commonly seen distribution in nature, education, and business. Data that are mounded or bell shaped are easily found across various fields of study. Although there is high utility with the normal distribution; often the full range can not be observed. The truncated normal distribution accounts for the inability to observe the full range and allows for inferring back to the original population. Depending on the amount of truncation, the truncated normal has several distinct shapes. A simulation study evaluating the performance of the maximum likelihood estimators and method of moment estimators is conducted and a …

Bayesian And Frequentist Approaches For The Analysis Of Multiple Endpoints Data Resulting From Exposure To Multiple Health Stressors., Epiphanie Nyirabahizi

Theses and Dissertations

In risk analysis, Benchmark dose (BMD)methodology is used to quantify the risk associated with exposure to stressors such as environmental chemicals. It consists of fitting a mathematical model to the exposure data and the BMD is the dose expected to result in a pre-specified response or benchmark response (BMR). Most available exposure data are from single chemical exposure, but living objects are exposed to multiple sources of hazards. Furthermore, in some studies, researchers may observe multiple endpoints on one subject. Statistical approaches to address multiple endpoints problem can be partitioned into a dimension reduction group and a dimension preservative group. …

Finite Element Approximations For Stokes-Darcy Flow With Beavers-Joseph Interface Conditions, Yanzhao Cao, Max Gunzburger, Xiaolong Hu, Fei Hua, Xiaoming Wang, Weidong Zhao

Mathematics and Statistics Faculty Research & Creative Works

Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. the coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. on the interface between the matrix and conduit, Beavers-Joseph interface conditions, instead of the simplified Beavers-Joseph-Saffman conditions, are imposed. Convergence and error estimates for finite element approximations are obtained. Numerical experiments illustrate the validity of the theoretical results. © 2010 Society for Industrial and Applied Mathematics.