Statistics and Probability Commons^™

Mathematical Engineering And Control With Applications, Mamdouh M. El Kady, Martin Bohner, J. Liang, Mouffak Benchohra

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

As Strong As The Weakest Link: Mining Diverse Cliques In Weighted Graphs, Petko Bogdanov, Ben Baumer, Prithwish Basu, Amotz Bar-Noy, Ambuj K. Singh

Statistical and Data Sciences: Faculty Publications

Mining for cliques in networks provides an essential tool for the discovery of strong associations among entities. Applications vary, from extracting core subgroups in team performance data arising in sports, entertainment, research and business; to the discovery of functional complexes in high-throughput gene interaction data. A challenge in all of these scenarios is the large size of real-world networks and the computational complexity associated with clique enumeration. Furthermore, when mining for multiple cliques within the same network, the results need to be diversified in order to extract meaningful information that is both comprehensive and representative of the whole dataset. We …

Revised Estimates Of World Wide Anemia, Kentron R. Wride, Dr. Gilbert W. Fellingham

Journal of Undergraduate Research

The stated mission of the World Health Organization (WHO) is to improve health around the world. One aspect of this mission involves preparing reliable models to describe patterns of health world wide. WHO has built a summary data file based on nearly 700 published and unpublished reports of anemia rates of women worldwide. Fellingham et. al (1996) prepared a preliminary report of the first model developed from this data as well as the resulting estimates of world wide anemia. The study was based on 448 records from 83 countries. The data included the mean hemoglobin concentration, sample size, a country …

Community College Consortium Promotes Open Educational Practices Through Outreach And Collaboration, Una T. Daly, Lisa Storm, Barbara Illowsky

SJSU Open Access Conference

The Community College Consortium for Open Educational Resources (CCCOER) is a community of practice focused on awareness and promoting best practices for OER discovery and adoption including open textbooks, open MOOCs, and open repositories to enhance learning and teaching. Through monthly outreach webinars with OER leaders and online advisory meetings, the community shares their projects and expertise encouraging collaboration across institutions, disciplines, and higher education sectors. Hear from the consortium director and two leaders of the community college OER movement.

• Una Daly, Director of Community College Outreach, OpenCourseWare Consortium. Building a community to promote awareness and shared knowledge of …

Hypothesis Testing For An Extended Cox Model With Time-Varying Coefficients, Takumi Saegusa, Chongzhi Di, Ying Qing Chen

UW Biostatistics Working Paper Series

The log-rank test has been widely used to test a treatment effect under the Cox model for censored time-to-event outcomes, though it may lose power substantially when the model's proportional hazards assumption does not hold. In this paper, we consider an extended Cox model that uses B-splines or smoothing splines to model a time-varying treatment effect and propose score test statistics for the treatment effect. Our proposed new tests combine statistical evidence from both the magnitude and the shape of the time-varying hazard ratio function, and thus are omnibus and powerful against various types of alternatives. In addition, the new …

Challenges In Estimating The Causal Effect Of An Intervention With Pre-Post Data (Part 1): Definition & Identification Of The Causal Parameter, Ann M. Weber, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

There is mixed evidence of the effectiveness of interventions operating on a large scale. Although the lack of consistent results is generally attributed to problems of implementation or governance of the program, the failure to find a statistically significant effect (or the success of finding one) may be due to choices made in the evaluation. To demonstrate the potential limitations and pitfalls of the usual analytic methods used for estimating causal effects, we apply the first half of a roadmap for causal inference to a pre-post evaluation of a community-level, national nutrition program. Selection into the program was non-random and …

Variable Importance And Prediction Methods For Longitudinal Problems With Missing Variables, Ivan Diaz, Alan E. Hubbard, Anna Decker, Mitchell Cohen

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper we present prediction and variable importance (VIM) methods for longitudinal data sets containing both continuous and binary exposures subject to missingness. We demonstrate the use of these methods for prognosis of medical outcomes of severe trauma patients, a field in which current medical practice involves rules of thumb and scoring methods that only use a few variables and ignore the dynamic and high-dimensional nature of trauma recovery. Well-principled prediction and VIM methods can thus provide a tool to make care decisions informed by the high-dimensional patient’s physiological and clinical history. Our VIM parameters can be causally interpreted …

The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz

Mathematics and Statistics Faculty Research & Creative Works

We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided. © 2013 Elsevier Ltd.

Targeted Learning Of An Optimal Dynamic Treatment, And Statistical Inference For Its Mean Outcome, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose we observe n independent and identically distributed observations of a time-dependent random variable consisting of baseline covariates, initial treatment and censoring indicator, intermediate covariates, subsequent treatment and censoring indicator, and a final outcome. For example, this could be data generated by a sequentially randomized controlled trial, where subjects are sequentially randomized to a first line and second line treatment, possibly assigned in response to an intermediate biomarker, and are subject to right-censoring. In this article we consider estimation of an optimal dynamic multiple time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, …

Sparse Median Graphs Estimation In A High Dimensional Semiparametric Model, Fang Han, Han Liu, Brian Caffo

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Utilizing the concept of median graphs in summarizing the commonality across these graphical structures, a novel semiparametric approach to modeling such complex aggregated data is provided along with robust estimation of the median graph, which is assumed to be sparse. The estimator is proved to be consistent in graph recovery and an upper bound on the rate of convergence is given. Experiments on both …

Growth Of Tropical Dasyatid Rays Estimated Using A Multi-Analytical Approach, Owen R. O'Shea, Matias Braccini, Rory Mcauley, Conrad W. Speed, Mark G. Meekan

Fisheries Research Articles

We studied the age and growth of four sympatric stingrays: reticulate whipray, Himanutra uarnak (n=19); blue mask, Neotrygon kuhlii (n=34); cowtail, Pastinachus atrus (n=32) and blue-spotted fantail, Taeniura lymma (n=40) rays at Ningaloo Reef, a fringing coral reef on the north-western coast of western Australia. Age estimates derived from band counts within sectioned vertebrae ranged between 1 and 27 years (H. uarnak, 1 - 25 yrs.; N. kuhlii, 1.5 - 13 yrs.; P. atrus, 1 - 27 yrs. and T. lymma, 1 -11 yrs.). Due to limitations of sample sizes, we combined several analytical methods …

Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales, Rabia Bibi, Martin Bohner, Josip Pečarić, Sanja Varǒsanec

Mathematics and Statistics Faculty Research & Creative Works

We obtain integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality. © ELEMENT, Zagreb.

Control Chart Development For The Coefficient Of Variation, Geraldine Madariaga, Dr. C. Shane Reese

Journal of Undergraduate Research

Industries use control charts to evaluate whether or not a process is “in control” or producing parts that meet the standards of quality. Control charts are based on the principle that variation between samples can be predicted based on sampling distributions. Parts are measured and the computed test statistic is plotted within limits that are based on the standard deviation or quantiles of the sampling distribution of the test statistic.

Adapting Data Adaptive Methods For Small, But High Dimensional Omic Data: Applications To Gwas/Ewas And More, Sara Kherad Pajouh, Alan E. Hubbard, Martyn T. Smith

U.C. Berkeley Division of Biostatistics Working Paper Series

Exploratory analysis of high dimensional "omics" data has received much attention since the explosion of high-throughput technology allows simultaneous screening of tens of thousands of characteristics (genomics, metabolomics, proteomics, adducts, etc., etc.). Part of this trend has been an increase in the dimension of exposure data in studies of environmental exposure and associated biomarkers. Though some of the general approaches, such as GWAS, are transferable, what has received less focus is 1) how to derive estimation of independent associations in the context of many competing causes, without resorting to a misspecified model, and 2) how to derive accurate small-sample inference …

Estimation Of Variation For High-Throughput Molecular Biological Experiments With Small Sample Size, Danni Yu

Open Access Dissertations

Motivation: In the quantification of molecular components, a large variation can affect and even potentially mislead the biological conclusions. Meanwhile, the high-throughput experiments often involve a small number of samples due to the limitation of cost and time. In such cases, the stochastic information may dominate the outcome of an experiment because there may not be enough samples to present the true biological information. It is challenging to distinguish the changes in phenotype from the stochastic variation.

Methods: Since the biological molecules have been quantified with different technologies, different statistical methods are required. Focusing on three types of important high-throughput …

Different Types Of Backward Bifurcations Due To Density-Dependent Treatments, Baojun Song, Wen Du, Jie Lou

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A set of deterministic SIS models with density-dependent treatments are studied to understand the disease dynamics when different treatment strategies are applied. Qualitative analyses are carried out in terms of general treatment functions. It has become customary that a backward bifurcation leads to bistable dynamics. However, this study finds that finds that bistability may not be an option at all; the disease-free equilibrium could be globally stable when there is a backward bifurcation. Furthermore, when a backward bifurcation occurs, the fashion of bistability could be the coexistence of either dual stable equilibria or the disease-free equilibrium and a stable limit …

The Spatial Distribution Of Cancer Incidence In Fars Province: A Gis-Based Analysis Of Cancer Registry Data, Ali Goli, Mahbobeh Oroei, Mehdi Jalalpour, Hossein Faramarzi, Mehrdad Askarian

Civil and Environmental Engineering Faculty Publications

Background: Cancer is a major health problem in the developing countries. Variations of its incidence rate among geographical areas are due to various contributing factors. This study was performed to assess the spatial patterns of cancer incidence in the Fars Province, based on cancer registry data and to determine geographical clusters.

Methods: In this cross sectional study, the new cases of cancer were recorded from 2001 to 2009. Crude incidence rate was estimated based on age groups and sex in the counties of the Fars Province. Age standardized incidence rates (ASR) per 100,000 was calculated in each year. …

Statistical Models For Gene And Transcripts Quantification And Identification Using Rna-Seq Technology, Han Wu

Open Access Dissertations

RNA-Seq has emerged as a powerful technique for transcriptome study. As much as the improved sensitivity and coverage, RNA-Seq also brings challenges for data analysis. The massive amount of sequence reads data, excessive variability, uncertainties, and bias and noises stemming from multiple sources all make the analysis of RAN-Seq data difficult. Despite much progress, RNA-Seq data analysis still has much room for improvement, especially on the quantification of gene and transcript expression levels. The quantification of gene expression level is a direct inference problem, whereas the quantification of the transcript expression level is an indirect problem, because the label of …

Non-Parametric Spatial Models, Cheng Liu

Open Access Dissertations

Covariance functions play a central role in spatial statistics. Parametric covariance functions have been used in most of the existing works on the analysis of spatial data. The primary reason for this is that the classes of parametric covariance functions guarantee that the fitted covariance function is positive definite. In this dissertation, I undertake two non-parametric approaches to modelling the covariance functions.

Our approach is motivated by problems that arise in spatial data analysis in recent years. First, it is nontrivial to choose a parametric family among many parametric families of covariance function. A non-parametric covariance function circumvents this problem. …

A Jackknife Empirical Likelihood Approach To Goodness Of Fit U-Statistic Testing With Side Information, Qun Lin

Open Access Dissertations

Motivated by applications to goodness of fit U-statistics testing, the jackknife empirical likelihood of Jing, et al. (2009) is justified with an alternative approach, and the Wilks theorem for vector U-statistics is proved. This generalizes Owen's empirical likelihood theorem for a vector mean to a vector U-statistics-based mean and includes the jackknife empirical likelihood of U-statistics with side information as a special case. The results are generalized to allow for the constraints to use estimated criteria functions and for the number of constraints to grow with the sample size. The latter is needed to handle naturally occurring nuisance parameters in …

Generation And Statistical Modeling Of Active Protein Chimeras: A Sequence Based Approach, Nicholas Fico

Open Access Dissertations

Generation of active protein chimeras is a valuable tool to probe the functional space of proteins. Statistical modeling is the next logical step, allowing us to build a model of gene fragment replaceability between species. In this thesis I begin to develop the statistical tools that are needed to systematically describe combinatorial protein libraries. I present three sets of diverse chimeric protein libraries developed using sequence information. The statistical model of the human N-Ras and human K-Ras-4B genes reveal a set previously unidetifed surface residues on the N-Ras G-Domain that may be involved in cellular localization. Statistical modeling of a …

Disk Diffusion Breakpoint Determination Using A Bayesian Nonparametric Variation Of The Errors-In-Variables Model, Glen Richard Depalma

Open Access Dissertations

Drug dilution (MIC) and disk diffusion (DIA) are the two most common antimicrobial susceptibility tests used by hospitals and clinics to determine an unknown pathogen's susceptibility to various antibiotics. Both tests use breakpoints to classify the pathogen as either susceptible, indeterminant, or resistant to each drug under consideration. While the determination of these drug-specific MIC classification breakpoints is straightforward, determination of comparable DIA breakpoints is not. It is this issue that motivates this research.

Traditionally, the error-rate bounded (ERB) method has been used to calibrate the two tests. This procedure involves determining DIA breakpoints which minimize the observed discrepancies between …

Asymptotically Unbiased Estimator Of The Informational Energy With Knn, Angel Caţaron, Răzvan Andonie, Chinmei Y. Chueh

All Faculty Scholarship for the College of the Sciences

Motivated by machine learning applications (e.g., classification, function approximation, feature extraction), in previous work, we have introduced a non- parametric estimator of Onicescu’s informational energy. Our method was based on the k-th nearest neighbor distances between the n sample points, where k is a fixed positive integer. In the present contribution, we discuss mathematical properties of this estimator. We show that our estimator is asymptotically unbiased and consistent. We provide further experimental results which illustrate the convergence of the estimator for standard distributions.

Characterizations Of Distribution Of Ratio Of Rayleigh Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distribution of the ratio of two independent Rayleigh random variables are presented. These characterizations are based, on a truncated moment; on hazard function; and on certain functions of order statistics.

Bootstrapped Deattenuated Correlation With Missing Data, Anna Veprinsky

Psychology Theses & Dissertations

Issues with correlation attenuation due to measurement error are well documented. A corresponding correction, the deattenuated correlation, has been known for over a century. For over a decade, researchers have been investigated the deattenuated correlation identifying factors impacting its performance. Nonetheless, the deattenuated correlation is underutilized. In addition, there is limited research concerning confidence intervals for the deattenuated correlation. Here, the bootstrapped deattenuated correlation with corresponding confidence intervals is investigated for simulation conditions not previously considered simultaneously: missing data and non-normal distributions. The bootstrap deattenuated correlation was assessed for relative bias, standard error, and 95% coverage probability for the percentile …

Regression Trees For Longitudinal Data, Madan Gopal Kundu, Jaroslaw Harezlak

COBRA Preprint Series

Often when a longitudinal change is studied in a population of interest we find that changes over time are heterogeneous (in terms of time and/or covariates' effect) and a traditional linear mixed effect model [Laird and Ware, 1982] on the entire population assuming common parametric form for covariates and time may not be applicable to the entire population. This is usually the case in studies when there are many possible predictors influencing the response trajectory. For example, Raudenbush [2001] used depression as an example to argue that it is incorrect to assume that all the people in a given population …

Operation Export A Study Of Small- To Mid-Size Export Manufacturing Businesses In The Philippines, Anthony J. Familia, Dr. Paul J. Fields

Journal of Undergraduate Research

Market globalization gives developing countries a better opportunity to start successful export manufacturing operations than ever before. However, because virtually no research exists on export manufacturing companies in developing countries, many micro-entrepreneurs are unable to tap into these vast international markets. Consequently, potential export manufacturers typically start small family businesses that struggle to stay afloat in their own local economies.

The Identity Of Socially Responsible Business, Ryan Quinn, Dr. David A. Whetten

Journal of Undergraduate Research

In the popular press of today’s business world, socially responsible business is a hot topic. Periodicals, books, mutual funds, associations, and countless other media, groups, and people tout socially responsible business as the “right” thing for forward-looking companies to do. Underlying all of the claims of benefits that come from social responsibility is the assumption that becoming a socially responsible company is a simple task that any firm can accomplish. The purpose of this study was to question that assumption. It may (or may not) be a simple task to acquire a socially responsible image, but to become a truly …

Data Analysis Using Regression Modeling: Visual Display And Setup Of Simple And Complex Statistical Models, Emil N. Coman, Maria A. Coman, Eugen Iordache, Russell Barbour, Lisa Dierker

Yale Day of Data

We present visual modeling solutions for testing simple and more advanced statistical hypotheses in any research field. All models can be directly specified in analytical software like Mplus or R.

Data analysis in any substantive field can be easily accomplished by translating statistical tests in the intuitive language of regression-based path diagrams with observed and unobserved variables. All models we presented can be directly specified and estimated in analytical software.

Students can particularly benefit from being taught the simple regression modeling setup of the path analytical method, as it empowers them to apply the techniques to any data to test …

Net Reclassification Index: A Misleading Measure Of Prediction Improvement, Margaret Sullivan Pepe, Holly Janes, Kathleen F. Kerr, Bruce M. Psaty

UW Biostatistics Working Paper Series

The evaluation of biomarkers to improve risk prediction is a common theme in modern research. Since its introduction in 2008, the net reclassification index (NRI) (Pencina et al. 2008, Pencina et al. 2011) has gained widespread use as a measure of prediction performance with over 1,200 citations as of June 30, 2013. The NRI is considered by some to be more sensitive to clinically important changes in risk than the traditional change in the AUC (Delta AUC) statistic (Hlatky et al. 2009). Recent statistical research has raised questions, however, about the validity of conclusions based on the NRI. (Hilden and …