Digital Commons Network^™

Comparative Genomic Hybridization Array Analysis, Annette M. Molinaro, Mark J. Van Der Laan, Dan H. Moore

U.C. Berkeley Division of Biostatistics Working Paper Series

At the present time, there is increasing evidence that cancer may be regulated by the number of copies of genes in tumor cells. Through microarray technology it is now possible to measure the number of copies of thousands of genes and gene segments in samples of chromosomal DNA. Microarray comparative genomic hybridization (array CGH) provides the opportunity to both measure DNA sequence copy number gains and losses and map these aberrations to the genomic sequence. Gains can signify the over-expression of oncogenes, genes which stimulate cell growth and have become hyperactive, while losses can signify under-expression of tumor suppressor genes, …

A Method To Identify Significant Clusters In Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Clustering algorithms have been widely applied to gene expression data. For both hierarchical and partitioning clustering algorithms, selecting the number of significant clusters is an important problem and many methods have been proposed. Existing methods for selecting the number of clusters tend to find only the global patterns in the data (e.g.: the over and under expressed genes). We have noted the need for a better method in the gene expression context, where small, biologically meaningful clusters can be difficult to identify. In this paper, we define a new criteria, Mean Split Silhouette (MSS), which is a measure of cluster …

Boundary Layers Associated With Incompressible Navier-Stokes Equations: The Noncharacteristic Boundary Case, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

The goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly non-characteristic, i.e., there is injection and/or suction everywhere at the boundary. Following earlier work on the boundary layer for linearized Navier-Stokes equations in the case where the boundaries are characteristic (non-slip at the boundary and non-permeable), we consider here the case where the boundary is permeable and thus non-characteristic. the form of the boundary layer and convergence results are derived in two cases: linearized equation and full nonlinear equations. We prove that there exists …

Inconsistency Of Resampling Algorithms For High Breakdown Regression Estimators And A New Algorithm, Douglas M. Hawkins, David J. Olive

Articles and Preprints

Since high breakdown estimators are impractical to compute exactly in large samples, approximate algorithms are used. The algorithm generally produces an estimator with a lower consistency rate and breakdown value than the exact theoretical estimator. This discrepancy grows with the sample size, with the implication that huge computations are needed for good approximations in large high-dimensioned samples

The workhorse for HBE has been the ‘elemental set’, or ‘basic resampling’ algorithm. This turns out to be completely ineffective in high dimensions with high levels of contamination. However, enriching it with a “concentration” step turns it into a method that is able …

Juries, Judges, And Punitive Damages: An Empirical Study, Theodore Eisenberg, Neil Lafountain, Brian Ostrom, David Rottman, Martin T. Wells

Cornell Law Faculty Publications

This Article, the first broad-based analysis of punitive damages in judge-tried cases, compares judge and jury performance in awarding punitive damages and in setting their levels. Data covering one year of judge and jury trial outcomes from forty-five of the nation's largest counties yield no substantial evidence that judges and juries differ in the rate at which they award punitive damages or in the central relation between the size of punitive awards and compensatory awards. The relation between punitive and compensatory awards in jury trials is strikingly similar to the relation in judge trials. For a given level of compensatory …

L-Arginine Uptake And Metabolism Following In Vivo Silica Exposure In Rat Lungs, Leif D. Nelin, Gary S. Krenz, Louis G. Chicoine, Christopher A. Dawson, Ralph M. Schapira

Mathematics, Statistics and Computer Science Faculty Research and Publications

Pulmonary inflammation increases nitric oxide (NO) production via inducible nitric oxide synthase (iNOS). This study was performed to determine some of the factors that affect the availability of the NOS substrate, L-arginine (L-arg), in the intact lung subjected to silica-induced inflammation. Nitrate production, as an index of NO production, was significantly greater in silica-exposed lungs (53.5 ± 12.1 nmol/90 min) compared with controls (22.5 ±5.1 nmol/90 min, P < 0.05). This was accompanied by greater (P< 0.0001) 90-min [³H]L-arg uptake (62 ± 3% control, 82 ± 1% silica), a significantly (P < 0.005) increased permeability-surface area product for L-arg(0.28 ± 0.05 ml/min control, 0.63 ± 0.07 ml/min silica), and asignificantly (P < 0.001) increased urea production (1.16 ± 0.08µmol/90 min control, 1.77 ± 0.06 µmol/90 min silica). There was no difference in eNOS protein between groups and eNOS mRNA was not detectable in either group, whereas silica exposure resulted in the appearance of both iNOS protein and mRNA. Silica exposure increased CAT-1 and CAT-2 mRNA ~ 8-fold compared with controls. We conclude that the increase in NO production in silica-exposed lungs was associated with increased L-arg uptake from the vasculature, presumably resulting from increased CAT-1 and CAT-2, and by increased L-arg metabolism via arginase.

An Adaptive Analysis Of Covariance Using Tree-Structured Regression, Gary L. Gadbury, H. K. Iyer, H. T. Schreuder

Mathematics and Statistics Faculty Research & Creative Works

In this article, we propose an adaptive procedure for testing for the effect of a factor of interest in the presence of one or more confounding variables in observational studies. It is especially relevant for applications where the factor of interest has a suspected causal relationship with a response. This procedure is not tied to linear modeling or normal distribution theory, and it offers a valuable alternative to traditional methods. It is suitable for applications where a factor of interest is categorical, and the response is continuous. Confounding variables may be continuous or categorical. The method is comprised of two …

Applications Of Robust Distances For Regression, David J. Olive

Articles and Preprints

The DD plot, introduced by Rousseeuw and Van Driessen (1999), is a plot of classical vs robust Mahalanobis distances: MD_i vs RD_i. The DD plot can be used as a diagnostic for multivariate normality and elliptical symmetry, and to assess the success of numerical transformations towards elliptical symmetry. In the regression context, many procedures can be adversely affected if strong nonlinearities are present in the predictors. Even if strong nonlinearities are present, the robust distances can be used to help visualize important regression models such as generalized linear models.

Orthogonal Arrays Of Strength Three From Regular 3-Wise Balanced Designs, Charles J. Colbourn, D. L. Kreher, John P. Mcsorley, D. R. Stinson

Articles and Preprints

The construction given in Kreher, J Combin Des 4 (1996) 67 is extended to obtain new infinite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction.

A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan

U.C. Berkeley Division of Biostatistics Working Paper Series

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …

Studying The Functional Genomics Of Stress Responses In Loblolly Pine With The Expresso Microarray Experiment Management System, Lenwood S. Heath, Naren Ramakrishnan, Ronald R. Sederoff, Ross W. Whetten, Boris I. Chevone, Craig Struble, Vincent Y. Jouenne, Dawei Chen, Leonel Van Zyl, Ruth Grene

Mathematics, Statistics and Computer Science Faculty Research and Publications

Conception, design, and implementation of cDNA microarray experiments present a variety of bioinformatics challenges for biologists and computational scientists. The multiple stages of data acquisition and analysis have motivated the design of Expresso, a system for microarray experiment management. Salient aspects of Expresso include support for clone replication and randomized placement; automatic gridding, extraction of expression data from each spot, and quality monitoring; flexible methods of combining data from individual spots into information about clones and functional categories; and the use of inductive logic programming for higher-level data analysis and mining. The development of Expresso is occurring in parallel with …

On Size Mappings, W. J. Charatonik, Alicja Samulewicz

Mathematics and Statistics Faculty Research & Creative Works

A real-valued mapping r from the hyperspace of all compact subsets of a givenmetric space X is called a size mapping if r({x}) = 0 for x ∈ X and r(A) ≤ r(B) if a ⊂ B. We investigate what continua admit an open or a monotone size mapping. Special attention is paid to the diameter mappings.

Regression Analysis Of Recurrent Gap Times With Time-Dependent Covariates, Ying Qing Chen, Mei-Cheng Wang, Yijian Huang

U.C. Berkeley Division of Biostatistics Working Paper Series

Individual subjects may experience recurrent events of same type over a relatively long period of time in a longitudinal study. Researchers are often interested in the distributional pattern of gaps between the successive recurrent events and their association with certain concomitant covariates as well. In this article, their probability structure is investigated in presence of censoring. According to the identified structure, we introduce the proportional reverse-time hazards models that allow arbitrary baseline function for every individual in the study, when the time-dependent covariates effect is of main interest. Appropriate inference procedures are proposed and studied to estimate the parameters of …

Estimating Causal Parameters In Marginal Structural Models With Unmeasured Confounders Using Instrumental Variables, Tanya A. Henneman, Mark Johannes Van Der Laan, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

For statisticians analyzing medical data, a significant problem in determining the causal effect of a treatment on a particular outcome of interest, is how to control for unmeasured confounders. Techniques using instrumental variables (IV) have been developed to estimate causal parameters in the presence of unmeasured confounders. In this paper we apply IV methods to both linear and non-linear marginal structural models. We study a specific class of generalized estimating equations that is appropriate to these data, and compare the performance of the resulting estimator to the standard IV method, a two-stage least squares procedure. Our results are applied to …

On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang

Mathematics and Statistics Faculty Publications

We show that any C^1,1 solution to the uniformly elliptic equation F(D²u) = 0 must belong to C^2,α, if the equation has the Liouville property.

Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller

Mathematics and Statistics Faculty Publications

Two domain functionals describing the averaged expectation of exit times and averaged variance of exit times of Brownian motion from a domain, respectively, are studied.

Absolutely Continuous Jacobi Operators, Steen Pedersen

Mathematics and Statistics Faculty Publications

No abstract provided.

Mixed Signals: Rational-Choice Theories Of Social Norms And The Pragmatics Of Explanation, W. Bradley Wendel

Cornell Law Faculty Publications

The question of how societies secure cooperation and order in the absence of state enforced sanctions has long vexed law and economics scholars. Recently the concept of social norms--informally enforced rules of behavior--has occupied the attention of a large number of these theorists, who are concerned with understanding why economically rational actors would bother to follow rules whose costs seem to outweigh their benefits. Because of the prestige (or at least trendiness) of law and economics, it seems that now everyone in the legal academy is talking about social norms. This burgeoning scholarship is closely related to a wider concern …

Adipose Depletion And Apoptosis Induced By Trans-10, Cis-12 Conjugated Linoleic Acid In Mice, Kimberly M. Hargrave, Changlong Li, Brett J. Meyer, Stephen D. Kachman, Diane L. Hartzell, Mary Anne Della-Fera, Jess Miner, Clifton A. Baile

Department of Statistics: Faculty Publications

Objective: To compare the effectiveness of a conjugated linoleic acid (CLA) isomer mixture (mCLA) with each main isomer [trans-10,cis-12 CLA (CLA10,12) and cis-9,trans-11 CLA (CLA9,11)] in causing body lipid loss and adipose tissue apoptosis.

Research Methods and Procedures: Mice selected over 16 generations for high (MH) or low (ML) energy expenditure and a control group (MC) were fed diets containing either soy oil or soy oil plus mCLA, CLA10,12, or CLA9,11 for 5 days in one study and 14 days in a second study.

Results: Mice fed mCLA or CLA10,12 had less body lipid (p _ 0.05), smaller retroperitoneal …

Generalized Moving Average Models And Applications In High Frequency Data, Shelton Peiris, David E. Allen, Aerambamoorthy Thavaneswaran

Research outputs pre 2011

This paper considers a new class of first order moving average type time series model with index δ (> 0) to describe some hidden features of a time series. It is shown that this class of models provides a valid, simple solution to a new direction of time series modelling. In particular, for suitably chosen parameters (coefficient β and index δ) this type of models could be used to describe data with low or high frequency components. Various new results associated with this class are given in a general form. A simulation study is carried out to justify the theory. …

On Legal Interpretations Of The Condorcet Jury Theorem, Paul H. Edelman

Vanderbilt Law School Faculty Publications

There has been a spate of interest in the application of the Condorcet Jury Theorem to issues in the law. This theorem holds that a majority vote among a suitably large body of voters, all of whom are more likely than not to vote correctly, will almost surely result in the correct outcome. Its uses have ranged from estimating the correct size of juries to justifying the voting of creditors in Chapter 11 reorganizations. While the mathematics is unassailable, the legal interpretation of the conclusion is dependent on the model of probability one uses when invoking the assumption that the …

Ua56/1 Fact Book, Wku Institutional Research

WKU Archives Records

Statistical and demographic profile of WKU.

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …

Tuberculosis Models With Fast And Slow Dynamics: The Role Of Close And Casual Contacts, Baojun Song, Carlos Castillo-Chavez, Juan Pablo Aparicio

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our …

Discrete Predictive Analysis In Probabilistic Safety Assessment, Paul Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

This paper presents methods for predicting future numbers of component failures for probabilistic safety assessments (PSAs). The research is motivated and illustrated by discrete failure data from the nuclear industry, including failure counts for emergency diesel generators, pumps, and motor operated valves. Failure counts are modeled with Poisson and binomial distributions. Multiple-failure environments create extra problems for predictive inference, and are a primary focus of this paper. Common cause failures (CCFs), in particular, refer to the simultaneous failure of system components due to an external event. CCF prediction is investigated, and approximate inference methods are derived for various CCF models.

Common Cause Failure Prediction Using Data Mapping, Paul H. Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

To estimate power plant reliability, a probabilistic safety assessment might combine failure data from various sites. Because dependent failures are a critical concern in the nuclear industry, combining failure data from component groups of different sizes is a challenging problem. One procedure, called data mapping, translates failure data across component group sizes. This includes common cause failures, which are simultaneous failure events of two or more components in a group. In this paper, we present methods for predicting future plant reliability using mapped common cause failure data. The prediction technique is motivated by discrete failure data from emergency diesel generators …

Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego

Department of Math & Statistics Faculty Publications

For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤_spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a …

On The Existence Of Nontrivial Solutions To Some Elliptic Variational Inequalities, Vy Khoi Le, Klaus Schmitt

Mathematics and Statistics Faculty Research & Creative Works

The paper is concerned with the existence of nontrivial solutions of the obstacle problem: u ε K: ∫Ω ▽u▽ (v - u) dx - λ ∫ Ω u (v - u) dx ≥ ∫ Ω p (x, u) (v - u) dx ∀x ε K, where K = {v ε Ho1(Ω): v ≤ Ψ a.e. on Ω}. By using a generalized mountain pass theorem for inequalities, we prove, subject to some restrictions on the obstacle Ψ, the existence of nontrivial solutions of the above inequality.

An Interactive Tutorial For Teaching Statistical Power, Christopher L. Aberson '99, Dale E. Berger, Michael R. Healy '04, Victoria L. Romero '07

CGU Faculty Publications and Research

This paper describes an interactive Web-based tutorial that supplements instruction on statistical power. This freely available tutorial provides several interactive exercises that guide students as they draw multiple samples from various populations and compare results for populations with differing parameters (for example, small standard deviation versus large standard deviation). The tutorial assignment includes diagnostic multiple-choice questions with feedback addressing misconceptions, and follow-up questions suitable for grading. The sampling exercises utilize an interactive Java applet that graphically demonstrates relationships between statistical power and effect size, null and alternative populations and sampling distributions, and Type I and II error rates. The applet …

Evaluating Java Applets For Teaching On The Internet, Michael R. Healy '04, Dale E. Berger, Victoria L. Romero '07, Christopher L. Aberson '99, Amanda Saw '11

CGU Faculty Publications and Research

The Web Interface for Statistics Education (http://wise.cgu.edu) is a website built around interactive tutorials designed to teach introductory and advanced statistical concepts. The tutorials use Java applets that dynamically illustrate the statistical concepts being taught. By using Java applets, we teach statistics in a manner not possible in a traditional classroom environment. In this paper, we provide examples of the applets, illustrate how students use them, and we report the outcome of a study that examined tutorial effectiveness as a learning tool.