Statistics and Probability Commons^™

Teaching A University Course On The Mathematics Of Gambling, Stewart N. Ethier, Fred M. Hoppe

UNLV Gaming Research & Review Journal

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a …

Assessing The Accuracy Of Approximate Confidence Intervals Proposed For The Mean Of Poisson Distribution, Alireza Shirvani, Malek Fathizadeh

Journal of Modern Applied Statistical Methods

The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.

Analytical Closed-Form Solution For General Factor With Many Variables, Stan Lipovetsky, Vladimir Manewitsch

Journal of Modern Applied Statistical Methods

The factor analytic triad method of one-factor solution gives the explicit analytical form for a common latent factor built by three variables. The current work considers analytical presentation of a general latent factor constructed in a closed-form solution for multivariate case. The results can be supportive to theoretical description and practical application of latent variable modeling, especially for big data because the analytical closed-form solution is not prone to data dimensionality.

Regression Modeling And Prediction By Individual Observations Versus Frequency, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

A regression model built by a dataset could sometimes demonstrate a low quality of fit and poor predictions of individual observations. However, using the frequencies of possible combinations of the predictors and the outcome, the same models with the same parameters may yield a high quality of fit and precise predictions for the frequencies of the outcome occurrence. Linear and logistical regressions are used to make an explicit exposition of the results of regression modeling and prediction.

Measuring Localization Confidence For Quantifying Accuracy And Heterogeneity In Single-Molecule Super-Resolution Microscopy, Hesam Mazidi, Tianben Ding, Arye Nehorai, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

We present a computational method, termed Wasserstein-induced flux (WIF), to robustly quantify the accuracy of individual localizations within a single-molecule localization microscopy (SMLM) dataset without ground- truth knowledge of the sample. WIF relies on the observation that accurate localizations are stable with respect to an arbitrary computational perturbation. Inspired by optimal transport theory, we measure the stability of individual localizations and develop an efficient optimization algorithm to compute WIF. We demonstrate the advantage of WIF in accurately quantifying imaging artifacts in high-density reconstruction of a tubulin network. WIF represents an advance in quantifying systematic errors with unknown and complex distributions, …

Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri

Spora: A Journal of Biomathematics

Bighead carp (Hypophthalmichthys nobilis) are an invasive, voracious, highly fecund species threatening the ecological integrity of the Great Lakes. This agent-based model and analysis explore bighead carp behavior in response to acoustic deterrence in an effort to discover properties that increase likelihood of deterrence system failure. Results indicate the most significant (p < 0.05) influences on barrier failure are the quantity of detritus and plankton behind the barrier, total number of bighead carp successfully deterred by the barrier, and number of native fishes freely moving throughout the simulation. Quantity of resources behind the barrier influence bighead carp to penetrate when populations are resource deprived. When native fish populations are low, an accumulation of phytoplankton can occur, increasing the likelihood of an algal bloom occurrence. Findings of this simulation suggest successful implementation with proper maintenance of an acoustic deterrence system has potential of abating the threat of bighead carp on ecological integrity of the Great Lakes.

Session 11 - Methods: Bootstrap Control Chart For Pareto Percentiles, Ruth Burkhalter

SDSU Data Science Symposium

Lifetime percentile is an important indicator of product reliability. However, the sampling distribution of a percentile estimator for any lifetime distribution is not a bell shaped one. As a result, the well-known Shewhart-type control chart cannot be applied to monitor the product lifetime percentiles. In this presentation, Bootstrap control charts based on maximum likelihood estimator (MLE) are proposed for monitoring Pareto percentiles. An intensive simulation study is conducted to compare the performance among the proposed MLE Bootstrap control chart and Shewhart-type control chart.

Evaluation Of Text Mining Techniques Using Twitter Data For Hurricane Disaster Resilience, Joshua Eason, Sathish Kumar

SDSU Data Science Symposium

Data obtained from social media microblogging websites such as Twitter provide the unique ability to collect and analyze conversations of the public in order to gain perspective on the thoughts and feelings of the general public. Sentiment and volume analysis techniques were applied to the dataset in order to gain an understanding of the amount and level of sentiment associated with certain disaster-related tweets, including a topical analysis of specific terms. This study showed that disaster-type events such as a hurricane can cause some strong negative sentiment in the period of time directly preceding the event, but ultimately returns quickly …

Asymptotic Simultaneous Estimations For Contrasts Of Quantiles, Lawrence Sethor Segbehoe, Frank Schaarschmidt, Gemechis Dilba Djira

SDSU Data Science Symposium

Although the expected value is popular, many researches in the health and social sciences involve skewed distributions and inferences concerning quantiles. Most standard multiple comparison procedures require the normality assumption. For example, few methods exist for comparing the medians of independent samples or quantiles of several distributions in general. To our knowledge, there is no general-purpose method for constructing simultaneous confidence intervals for multiple contrasts of quantiles. In this paper, we develop an asymptotic method for constructing such intervals and extend the idea to that of time-to-event data in survival analysis. Small-sample performance of the proposed method is assessed in …

Exploration Of Factors Associated With Perceptions Of Community Safety Among Youth In Hillsborough County, Florida: A Convergent Parallel Mixed-Methods Approach, Yingwei Yang

USF Tampa Graduate Theses and Dissertations

Introduction: Youth perceived safety is not only linked to crime and violence in a neighborhood but is also associated with health risk behaviors and certain neighborhood characteristics. The purpose of this mixed-methods study was to measure the co-occurring effects of individual and community risk factors by conducting a secondary data analysis using structural equation modeling (SEM) and to explore reasons for youth feeling safe/unsafe in their community using photovoice methodology.

Methods: Syndemic theory/model served as the theoretical framework to guide this mixed-methods study with a convergent parallel design. The quantitative strand (first manuscript) utilized an existing dataset collected from middle …

Comparison Of Upper Extremity Function In Women With And Women Without A History Of Breast Cancer, Mary Insana Fisher, Gilson J. Capilouto, Terry Malone, Heather M. Bush, Timothy L. Uhl

Communication Sciences and Disorders Faculty Publications

Background

Breast cancer treatments often result in upper extremity functional limitations in both the short and long term. Current evidence makes comparisons against a baseline or contralateral limb, but does not consider changes in function associated with aging.

Objective

The objective of this study was to compare upper extremity function between women treated for breast cancer more than 12 months in the past and women without cancer.

Design

This was an observational cross-sectional study.

Methods

Women who were diagnosed with breast cancer and had a mean post-surgical treatment time of 51 months (range = 12–336 months) were compared with women …

Bayesian Reliability Analysis Of The Power Law Process And Statistical Modeling Of Computer And Network Vulnerabilities With Cybersecurity Application, Freeh N. Alenezi

USF Tampa Graduate Theses and Dissertations

As most of mankind now lives in an era of high dependence on multiple technologies and complex systems to store and manage sensitive information, researchers are constantly urged to obtain and improve measurements and methodologies that have the ability to evaluate systems reliability and security. The objectives of the present dissertation are to improve the Bayesian reliability estimation of a software package where the Power Law Process, also known as Non-Homogeneous Poisson Process, is the underlying failure model and to develop a set of statistical models evaluating computer operating systems vulnerabilities. Furthermore, we develop a reliability function of a computer …

Hierarchical Clustering Analyses Of Plasma Proteins In Subjects With Cardiovascular Risk Factors Identify Informative Subsets Based On Differential Levels Of Angiogenic And Inflammatory Biomarkers, Zachary Winder, Tiffany L. Sudduth, David W. Fardo, Qiang Cheng, Larry B. Goldstein, Peter T. Nelson, Frederick A. Schmitt, Gregory A. Jicha, Donna M. Wilcock

Sanders-Brown Center on Aging Faculty Publications

Agglomerative hierarchical clustering analysis (HCA) is a commonly used unsupervised machine learning approach for identifying informative natural clusters of observations. HCA is performed by calculating a pairwise dissimilarity matrix and then clustering similar observations until all observations are grouped within a cluster. Verifying the empirical clusters produced by HCA is complex and not well studied in biomedical applications. Here, we demonstrate the comparability of a novel HCA technique with one that was used in previous biomedical applications while applying both techniques to plasma angiogenic (FGF, FLT, PIGF, Tie-2, VEGF, VEGF-D) and inflammatory (MMP1, MMP3, MMP9, IL8, TNFα) protein data to …

Informal Professional Development On Twitter: Exploring The Online Communities Of Mathematics Educators, Jaymie Ruddock

SMU Journal of Undergraduate Research

Professional development in its most traditional form is a classroom setting with a lecturer and an overwhelming amount of information. It is no surprise, then, that informal professional development away from institutions and on the teacher's own terms is a growing phenomenon due to an increased presence of educators on social media. These communities of educators use hashtags to broadcast to each other, with general hashtags such as #edchat having the broadest audience. However, many math educators usethe hashtags #ITeachMath and #MTBoS, communities I was interested in learning more about. I built a python script that used Tweepy to connect …

Sufficient Dimension Folding In Regression Via Distance Covariance For Matrix‐Valued Predictors, Wenhui Sheng, Qingcong Yuan

Mathematical and Statistical Science Faculty Research and Publications

In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we …

Mathematical Modelling Of The Tuberculosis Epidemiology, Ally Yeketi Ayinla

Student Works (2020-2029)

This project analyses the tuberculosis (TB) epidemic mathematically using compartmental modelling approach. Three models are presented to discuss drug susceptible and multi-drug resistant TB. The first model presented has 4 compartments; susceptible, exposed, infectious and recovered. The relevance of the exposed class in managing TB is analysed and found to be useful in delaying the eventual onset of the infection. Compared to previous researches, our results significantly show that when efforts are made such that no infected individual bypasses the exposed class and progresses directly to the infectious, the TB epidemic is successfully combatted. Also, the model is used to …

Predicting Class-Imbalanced Business Risk Using Resampling, Regularization, And Model Ensembling Algorithms, Yan Wang, Sherry Ni

Published and Grey Literature from PhD Candidates

We aim at developing and improving the imbalanced business risk modeling via jointly using proper evaluation criteria, resampling, cross-validation, classifier regularization, and ensembling techniques. Area Under the Receiver Operating Characteristic Curve (AUC of ROC) is used for model comparison based on 10-fold cross-validation. Two undersampling strategies including random undersampling (RUS) and cluster centroid undersampling (CCUS), as well as two oversampling methods including random oversampling (ROS) and Synthetic Minority Oversampling Technique (SMOTE), are applied. Three highly interpretable classifiers, including logistic regression without regularization (LR), L1-regularized LR (L1LR), and decision tree (DT) are implemented. Two ensembling techniques, including Bagging and Boosting, are …

A Xgboost Risk Model Via Feature Selection And Bayesian Hyper-Parameter Optimization, Yan Wang, Sherry Ni

Published and Grey Literature from PhD Candidates

This paper aims to explore models based on the extreme gradient boosting (XGBoost) approach for business risk classification. Feature selection (FS) algorithms and hyper-parameter optimizations are simultaneously considered during model training. The five most commonly used FS methods including weight by Gini, weight by Chi-square, hierarchical variable clustering, weight by correlation, and weight by information are applied to alleviate the effect of redundant features. Two hyper-parameter optimization approaches, random search (RS) and Bayesian tree-structuredParzen Estimator (TPE), are applied in XGBoost. The effect of different FS and hyper-parameter optimization methods on the model performance are investigated by the Wilcoxon Signed Rank …

An Automatic Interaction Detection Hybrid Model For Bankcard Response Classification, Yan Wang, Sherry Ni, Brian Stone

Published and Grey Literature from PhD Candidates

Data mining techniques have numerous applications in bankcard response modeling. Logistic regression has been used as the standard modeling tool in the financial industry because of its almost always desirable performance and its interpretability. In this paper, we propose a hybrid bankcard response model, which integrates decision tree-based chi-square automatic interaction detection (CHAID) into logistic regression. In the first stage of the hybrid model, CHAID analysis is used to detect the possible potential variable interactions. Then in the second stage, these potential interactions are served as the additional input variables in logistic regression. The motivation of the proposed hybrid model …

A Two-Stage Hybrid Model By Using Artificial Neural Networks As Feature Construction Algorithms, Yan Wang, Sherry Ni, Brian Stone

Published and Grey Literature from PhD Candidates

We propose a two-stage hybrid approach with neural networks as the new feature construction algorithms for bankcard response classifications. The hybrid model uses a very simple neural network structure as the new feature construction tool in the first stage, then the newly created features are used as the additional input variables in logistic regression in the second stage. The model is compared with the traditional one-stage model in credit customer response classification. It is observed that the proposed two-stage model outperforms the one-stage model in terms of accuracy, the area under the ROC curve, and KS statistic. By creating new …

Developing And Improving Risk Models Using Machine-Learning Based Algorithms, Yan Wang, Sherry Ni

Published and Grey Literature from PhD Candidates

The objective of this study is to develop a good risk model for classifying business delinquency by simultaneously exploring several machine learning-based methods including regularization, hyperparameter optimization, and model ensembling algorithms. The rationale under the analyses is firstly to obtain good base binary classifiers (include Logistic Regression (LR), K-Nearest Neighbors (KNN ), Decision Tree (DT), and Artificial Neural Networks (ANN )) via regularization and appropriate settings of hyper-parameters. Then two model ensembling algorithms including bagging and boosting are performed on the good base classifiers for further model improvement. The models are evaluated using accuracy, Area Under the Receiver Operating Characteristic …

Pair-A-Dice Lost: Experiments In Dice Control, Robert H. Scott Iii, Donald R. Smith

UNLV Gaming Research & Review Journal

This paper presents our findings from experiments designed to test whether we could use a custom-made dice throwing machine applying common dice control methods to produce dice rolls that differ from random. In earlier research we calculated the percentages of control a craps player needs to break even or beat the house (Smith and Scott, 2018). Using the most common practices of dice control in craps, we established how dice should be configured (i.e., set) and thrown to achieve certain outcomes such as not rolling a seven in the point cycle. We decided to run experiments to see if a …

Mentoring Multi-College Bystander Efficacy Evaluation – An Approach To Growing The Next Generation Of Gender-Based Interpersonal Violence Intervention And Prevention (Vip) Researchers, Ann L. Coker, Danielle Davidov, Heather M. Bush, Emily R. Clear

Obstetrics and Gynecology Faculty Publications

The Centers for Disease Control and Prevention provided funding (U01 CE002668) to evaluate bystander program efficacy to reduce gender-based violence on college campuses (Aim 1) and to create a mentoring network (Aim 2) for young campus-based researchers interested in violence intervention or prevention (VIP). While an evaluation of this mentoring program is ongoing, our purpose here was to document the strategies used to create, implement, and begin evaluation of this national multi-college mentoring network. As each public college was recruited into this evaluation named multi-college Bystander Efficacy Evaluation (mcBEE), each college was invited to nominate a researcher interested in receiving …

Art, Artfulness, Or Artifice?: A Review Of The Art Of Statistics: How To Learn From Data, By David Spiegelhalter, Jason Makansi

Numeracy

David Spiegelhalter. 2019. The Art of Statistics: How to Learn From Data. (London: The Penguin Group). 444 pp. ISBN 978-1541618510

The author successfully eases the reader away from the rigor of statistical methods and calculations and into the realm of statistical thinking. Despite an engaging style and attention-grabbing examples, the reader of The Art of Statistics will need more than a casual grounding in statistics to get what Spiegelhalter, I believe, intends from his book. It should be viewed as a companion to a more rigorous textbook on statistical methods but not necessarily a book that makes statistics any …

The Author’S Reflections On No B.S. (Bad Stats): Black People Need People Who Believe In Black People Enough Not To Believe Every Bad Thing They Hear About Black People, Ivory A. Toldson

Numeracy

Toldson, Ivory. A. 2019. No BS (Bad Stats): Black People Need People Who Believe in Black People Enough Not to Believe Every Bad Thing They Hear About Black People (Boston, MA: Brill-Sense) 194 pp. ISBN 978-9004397026.

This essay provides an introduction to No BS (Bad Stats): Black People Need People Who Believe in Black People Enough Not to Believe Every Bad Thing They Hear About Black People. In the essay, the author discusses how cynical views about the educational potential of Black children motivated him to write a book that challenges negative statistics. The essay also outlines the harmful …

Effects Of Quantitative Literacy On Healthcare Decision-Making: An Aural Context, Robert G. Root, Sonia Bhala

Numeracy

We propose a relationship between sensory modality, numerical formatting, and performance on a survey simulating healthcare decision-making. We examine the current literature on aural health literacy, and specifically aural literacy coupled with health numeracy. We then create a survey instrument called the Bhala test for this purpose and demonstrate that it is moderately internally consistent and provides results that correlate with the NUMi assessment, a widely accepted measure of health numeracy. The quantitative information provided in the Bhala test has two treatments, percentage and natural frequency formats, in an effort to determine which format is easier for subjects to use …

Estimating Marginal Hazard Ratios By Simultaneously Using A Set Of Propensity Score Models: A Multiply Robust Approach, Di Shu, Peisong Han, Rui Wang, Sengwee Toh

Harvard University Biostatistics Working Paper Series

The inverse probability weighted Cox model is frequently used to estimate marginal hazard ratios. Its validity requires a crucial condition that the propensity score model is correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to …

Using Hac Estimators For Intervention Analysis, Ashok K. Singh, Rohan J. Dalpatadu

Hospitality Faculty Research

The purpose of this article is to present an alternative method for intervention analysis of time series data that is simpler to use than the traditional method of fitting an explanatory Autoregressive Integrated Moving Average (ARIMA) model. Time series regression analysis is commonly used to test the effect of an event on a time series. An econometric modeling method, which uses a heteroskedasticity and autocorrelation consistent (HAC) estimator of the covariance matrix instead of fitting an ARIMA model, is proposed as an alternative. The method of parametric bootstrap is used to compare the two approaches for intervention analysis. The results …

Hypercholesterolemia Accelerates Both The Initiation And Progression Of Angiotensin Ii-Induced Abdominal Aortic Aneurysms, Jing Liu, Hisashi Sawada, Deborah A. Howatt, Jessica J. Moorleghen, Olga A. Vsevolozhskaya, Alan Daugherty, Hong S. Lu

Pharmacology and Nutritional Sciences Faculty Publications

Objective: This study determined whether hypercholesterolemia would contribute to both the initiation and progression of angiotensin (Ang)II-induced abdominal aortic aneurysms (AAAs) in mice.

Methods and Results: To determine whether hypercholesterolemia accelerates the initiation of AAAs, male low-density lipoprotein (LDL) receptor -/- mice were either fed one week of Western diet prior to starting AngII infusion or initiated Western diet one week after starting AngII infusion. During the first week of AngII infusion, mice fed normal diet had less luminal expansion of the suprarenal aorta compared to those initiated Western diet after the first week of AngII infusion. The two groups …

Estimation Of Conditional Power For Cluster-Randomized Trials With Interval-Censored Endpoints, Kaitlyn Cook, Rui Wang

Harvard University Biostatistics Working Paper Series

Cluster-randomized trials (CRTs) of infectious disease preventions often yield correlated, interval-censored data: dependencies may exist between observations from the same cluster, and event occurrence may be assessed only at intermittent clinic visits. This data structure must be accounted for when conducting interim monitoring and futility assessment for CRTs. In this article, we propose a flexible framework for conditional power estimation when outcomes are correlated and interval-censored. Under the assumption that the survival times follow a shared frailty model, we first characterize the correspondence between the marginal and cluster-conditional survival functions, and then use this relationship to semiparametrically estimate the cluster-specific …