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 …

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 …

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 …

On Improving Performance Of The Binary Logistic Regression Classifier, Michael Chang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Logistic Regression, being both a predictive and an explanatory method, is one of the most commonly used statistical and machine learning method in almost all disciplines. There are many situations, however, when the accuracies of the fitted model are low for predicting either the success event or the failure event. Several statistical and machine learning approaches exist in the literature to handle these situations. This thesis presents several new approaches to improve the performance of the fitted model, and the proposed methods have been applied to real datasets.

Transformations of predictors is a common approach in fitting multiple linear and …

Evaluating Parents Sociodemographic Factors And Childhood Vaccine Decisions, Mehret Girmay

UNLV Theses, Dissertations, Professional Papers, and Capstones

Vaccination is considered one of the most successful public health achievements of the 20th century. However, with increasing vaccine skepticism emerging over the past decades, there is a threat to the ongoing sustainment of vaccine coverage within all US communities. This study evaluated and compared parents’ sociodemographic factors associated with childhood vaccine decisions. This study is a secondary analysis of 893 parents/guardians, age 18-55 years with child(ren) < 7 years living in the U.S.

Predictive analysis was conducted using multinomial logistic regression modeling was used to examine vaccine decisions (accept, hesitant, and refuse) in relation to parents’ sociodemographic factors. Overall, (66.6%) of parents accepted recommended vaccines, while …

Trends And Disparities In Self-Reported And Measured Osteoporosis Among Us Adults, 2007-2014., Qing Wu, Yingke Xu, Ge Lin

Environmental & Global Health Faculty Research

(1) Background: Studies examining osteoporosis trends among US adults by different socioeconomic status (SES) are limited. The prevalence of self-reported osteoporosis in the US is rarely reported. (2) Methods: Data from the National Health and Nutritional Examination Survey (NHANES) between 2007–2008 and 2013–2014 cycles were analyzed. Age-adjusted prevalence of self-reported and that of measured osteoporosis were calculated overall and by sex, race/ethnicity, education attainment, and SES. (3) Results: The prevalence of self-reported osteoporosis was higher than that of measured osteoporosis in all three survey cycles for women, and in 2007–2008 and 2009–2010 for men. Participants with high school/GED or higher …

Biological And Practical Implications Of Genome-Wide Association Study Of Schizophrenia Using Bayesian Variable Selection, Benazir Rowe, Xiangning Chen, Zuoheng Wang, Jingchun Chen, Amei Amei

School of Medicine Faculty Research

Genome-wide association studies (GWAS) have identified over 100 loci associated with schizophrenia. Most of these studies test genetic variants for association one at a time. In this study, we performed GWAS of the molecular genetics of schizophrenia (MGS) dataset with 5334 subjects using multivariate Bayesian variable selection (BVS) method Posterior Inference via Model Averaging and Subset Selection (piMASS) and compared our results with the previous univariate analysis of the MGS dataset. We showed that piMASS can improve the power of detecting schizophrenia-associated SNPs, potentially leading to new discoveries from existing data without increasing the sample size. We tested SNPs in …

New Measure Of Skewness Of A Probability Distribution, Ashok Singh, Laxmi Gewali, Jiwan Khatiwada

Hospitality Faculty Research

Symmetry of the underlying probability density plays an important role in statistical inference, since the sampling distribution of the sample mean for a given sample size is more likely to be approximately normal for a symmetric distribution than for an asymmetric one. In this article, two new measures of skewness are proposed and the confidence intervals for true skewness are obtained via Monte Carlo simulation experiments. One advantage of the two proposed skewness measures over the standard measures of skewness is that the proposed measures of skewness take values inside the range (-1, +1).

Factors Associated With Eosinophilic Esophagitis In Nevada, Julia Lorraine Anderson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Eosinophilic esophagitis (EoE) is a rare immune-mediated illness with symptoms that range from difficulty swallowing to food impaction of the esophagus. Most published studies have been documented among patients residing in cool regions with significant annual rainfall. No published studies to our knowledge have been performed examining the healthcare utilization trends of EoE in Nevada. Utilizing two unique databases, the factors associated with EoE healthcare utilization patterns in Nevada were examined. All analyses were performed in R version 3.5.1. This study included a demographic and regional analysis identifying risk factors associated with having an EoE healthcare visit in Nevada. Several …

A Statistical Analysis Of The Roulette Martingale System: Examples, Formulas And Simulations With R, Peter Pflaumer

International Conference on Gambling & Risk Taking

Some gamblers use a martingale or doubling strategy as a way of improving their chances of winning. This paper derives important formulas for the martingale strategy, such as the distribution, the expected value, the standard deviation of the profit, the risk of a loss or the expected bet of one or multiple martingale rounds. A computer simulation study with R of the doubling strategy is presented. The results of doubling to gambling with a constant sized bet on simple chances (red or black numbers, even or odd numbers, and low (1 – 18) or high (19 – 36) numbers) and …

Kelly Fraction Estimation For Multiple Correlated Bets, William Chin

International Conference on Gambling & Risk Taking

It is well-known that expected portfolio growth is maximized by maximizing

expected logarithmic utility. This investment criterion is known as Kelly betting.

It has many optimality properties but is considered to be risky. Blackjack

teams and other advantage gamblers practice a fraction of the Kelly optimal to

decrease risk. Some hedge fund managers are thought to practice according to

Kelly principles. We use a continuous multivariate Geometric Brownian motion

model and present an interval estimate for the historical fraction for a portfolio

of correlated bets, possibly including a risk-free asset. Historical data comes

from a range of sources and the …

An Analysis Of Postmastectomy Breast Reconstruction Due To Breast Cancer In Nevada And The United States From 2008-2013, Jenna Webb

UNLV Theses, Dissertations, Professional Papers, and Capstones

Background: In the United States, female breast cancer was the leading cause of new cancer cases from 2011-2015. Since the Women’s Health and Cancer Act of 1998 (WHCRA), the federal government mandates employee and private health insurance providers to cover breast reconstruction if they cover mastectomies. Postmastectomy breast reconstruction (PBR) rates increased after the WHCRA, but these rates have remained relatively low throughout recent years. Objective: The objective of this study was to determine factors associated with women having PBR due to breast cancer in Nevada and the United States from 2008 to 2013. Methods: Using two HCUP database, NIS …

Telomeres, Nutrition And Mortality: Risk Factors For The Rate Of Telomere Length Decline And The Associations Between Telomere Length, Nutrition And Mortality, Saruna Ghimire

UNLV Theses, Dissertations, Professional Papers, and Capstones

Introduction: Telomeres are nucleoprotein structures located at the ends of eukaryotic chromosomes, thought to protect the DNA from damage. As a person experiences stressors, harmful exposures, and other diseases throughout their life, telomeres are thought to become damaged and their length shortened, decreasing their ability to protect the DNA. Nutrition is an important aspect of healthy aging. Preservation of telomere length (TL) is thought to be one of the mechanisms by which good nutrition can delay or prevent the development of chronic disease and death. Recent evidence of preservation of TL with good nutrition is promising. Thus, the aim of …

K-Tuple Sampling From Partially Rank-Ordered Sets, Marvin Javier

UNLV Theses, Dissertations, Professional Papers, and Capstones

With the introduction of Ranked Set Sampling (RSS), McIntyre (1952) demonstrated that using ranking information to select units for measurement can lead to estimators with reduced variance when compared to their counterparts based on a simple random sample of the same size. This is done by selecting a set of units, and without direct measurement, ranking the units in the set before identifying one unit for measurement. This ranking of the units can be done through judgement ranking (such as visual assessment), or by using a correlated auxiliary variable.

In its original form, RSS does not allow for ties when …

Health Disparities Among Sexual And Gender Minorities, Jennifer Keeley

UNLV Theses, Dissertations, Professional Papers, and Capstones

Decades of research has shown that sexual and gender minorities (SGMs) experience adverse health and mental health outcomes to a greater extent than their heterosexual peers. The need to better understand and eliminate health disparities in the SGM population was recognized by the National Institute on Minority Health and Health Disparities (NIMHD) at NIH. The Secretary of Health at the Department of Health and Human Services approved the designation of the SGM population as a health disparities population in 2016 and called for SGM studies to examine the health needs of the SGM population across SGM subgroups via large representative …

The Effects Of Injury On Running Status And Gait Biomechanics, Kristyne Wiegand

UNLV Theses, Dissertations, Professional Papers, and Capstones

Over the past several decades, endurance running has grown steadily as a popular form of physical activity. Running is easily accessible, does not require expensive equipment, and can be performed without specific skill training. Individuals who run also experience health benefits like increased cardiovascular health and reduced risk of all-cause morbidity. Despite these benefits, running is also associated with high rates of musculoskeletal injury. Although researchers have attempted to identify injury risks and mitigate the incidence of running injury, there is still no consensus as to why runners become injured. Research has also attempted to identify biomechanical movement patterns that …

Contributions To Mcmc Methods In Constrained Domains With Applications To Neuroimaging, Sharang Chaudhry

UNLV Theses, Dissertations, Professional Papers, and Capstones

Markov chain Monte Carlo (MCMC) methods form a rich class of computational techniques that help its user ascertain samples from target distributions when direct sampling is not possible or when their closed forms are intractable. Over the years, MCMC methods have been used in innumerable situations due to their flexibility and generalizability, even in situations involving nonlinear and/or highly parametrized models. In this dissertation, two major works relating to MCMC methods are presented.

The first involves the development of a method to identify the number and directions of nerve fibers using diffusion-weighted MRI measurements. For this, the biological problem is …

Capturing Heterogeneity Of Covariate Effects In Hidden Subpopulations In The Presence Of Censoring And Large Number Of Covariates, Farhad Shokoohi, Abbas Khalili, Masoud Asgharian, Shili Lin

Mathematical Sciences Faculty Research

The advent of modern technology has led to a surge of high-dimensional data in biology and health sciences such as genomics, epigenomics and medicine. The high-grade serous ovarian cancer (HGS-OvCa) data reported by The Cancer Genome Atlas (TCGA) Research Network is one example. The TCGA and other research groups have analyzed several aspects of these data. Here we study the relationship between Disease Free Time (DFT) after surgery among ovarian cancer patients and their DNA methylation profiles of genomic features. Such studies pose additional challenges beyond the typical big data problem due to population substructure and censoring. Despite the availability …

Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee

UNLV Gaming Research & Review Journal

There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. Is there a systematic way to derive such a hand-rank table? We show that there is indeed, and it involves finding the exact optimal …

Estimation Of The Parameters In A Spatial Regressive-Autoregressive Model Using Ord's Eigenvalue Method, Sajib Mahmud Mahmud Tonmoy

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we study one of Ord's (1975) global spatial regression models.

Ord considered spatial regressive-autoregressive models to describe the interaction

between location and a response variable in the presence of several covariates. He also

developed a practical estimation method for the parameters of this regression model

using the eigenvalues of a weight matrix that captures the contiguity of locations.

We review the theoretical aspects of his estimation method and implement it in the

statistical package R.

We also implement Ord's methods on the Columbus, Ohio, crime data set from the

year 1980, which involves the crime rate of …

Variations In Institutional Review Board Processes And Consent Requirements For Trauma Research: An East Multicenter Survey, Jeffry Nahmias, Areg Grigorian, Scott Brakenridge, Randeep S. Jawa, Daniel N. Holena, John Varujan Agapian, Brandon Bruns, Paul J. Chestovich, Bruce Chung, Jonathan Nguyen, Carl I. Schulman, Kristan Staudenmayer, Rachel Dixon, Jason W. Smith, Andrew C. Bernard, Jose L. Pascual

School of Medicine Faculty Research

Oversight of human subject research has evolved considerably since its inception. However, previous studies identified a lack of consistency of institutional review board (IRB) determination for the type of review required and whether informed consent is necessary, especially for prospective observational studies, which pose minimal risk of harm. We hypothesized that there is significant inter-institution variation in IRB requirements for the type of review and necessity of informed consent, especially for prospective observational trials without blood/tissue utilization. We also sought to describe investigators’ and IRB members’ attitudes toward the type of review and need for consent. Eastern Association for the …

Bi-Directional Testing For Change Point Detection In Poisson Processes, Moinak Bhaduri

UNLV Theses, Dissertations, Professional Papers, and Capstones

Point processes often serve as a natural language to chronicle an event's temporal evolution, and significant changes in the flow, synonymous with non-stationarity, are usually triggered by assignable and frequently preventable causes, often heralding devastating ramifications. Examples include amplified restlessness of a volcano, increased frequencies of airplane crashes, hurricanes, mining mishaps, among others. Guessing these time points of changes, therefore, merits utmost care. Switching the way time traditionally propagates, we posit a new genre of bidirectional tests which, despite a frugal construct, prove to be exceedingly efficient in culling out non-stationarity under a wide spectrum of environments. A journey surveying …

Fundamental Tradeoffs In Estimation Of Finite-State Hidden Markov Models, Justin Le

UNLV Theses, Dissertations, Professional Papers, and Capstones

Hidden Markov models (HMMs) constitute a broad and flexible class of statistical models that are widely used in studying processes that evolve over time and are only observable through the collection of noisy data. Two problems are essential to the use of HMMs: state estimation and parameter estimation. In state estimation, an algorithm estimates the sequence of states of the process that most likely generated a certain sequence of observations in the data. In parameter estimation, an algorithm computes the probability distributions that govern the time-evolution of states and the sampling of data. Although algorithms for the two problems are …

Prostate Cancer Survival Among Hispanics: A Surveillance, Epidemiology, And End Results (Seer) Population-Based Cohort Study, David Rivas

UNLV Theses, Dissertations, Professional Papers, and Capstones

Hispanics are now the youngest, largest, and fastest growing minority group in the U.S. Prostate cancer (PC) is the most commonly diagnosed cancer in men and is the second-leading cause of cancer deaths among Hispanics. For the first time, we examined PC-specific survival among distinct Hispanic groups that include Mexicans, Cubans, Dominicans, Puerto Ricans, as well as Central and South Americans. We compared these groups to the main reference population in the U.S., non-Hispanic Whites (NHW), after adjustment for prognostic factor risk categories (prostate-specific antigen (PSA) level, Gleason score, and tumor stage), as well as sociodemographic covariates (e.g., health insurance, …

Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii

UNLV Gaming Research & Review Journal

This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting …

Apolipoprotein-Defined Lipoprotein Subclasses, Serum Apolipoproteins, And Carotid Intima-Media Thickness In T1d, Arpita Basu, Alicia J. Jenkins, Julie A. Stoner, Ying Zhang, Richrd L. Klein

Kinesiology and Nutrition Sciences Faculty Research

Circulating apolipoprotein-defined lipoprotein subclasses (ADLS) and apolipoproteins predict vascular events in the general and type 2 diabetes populations, but data in T1D are limited. We examined associations of ADLS, serum apolipoproteins, and conventional lipids with carotid intima-media thickness (IMT) measured contemporaneously and 6 years later in 417 T1D participants [men: n = 269, age 42 +/- 6 y (mean +/- SD); women: n = 148, age 39 +/- 8 y] in the Epidemiology of Diabetes Interventions and Complications study, the follow-up of the Diabetes Control and Complications Trial (DCCT). Date were analyzed by multiple linear regression stratified by sex, and …

Biomarker And Clinical Trial Design Support For Disease-Modifying Therapies: Report Of A Survey Of The Eu/Us: Alzheimer's Disease Task Force, Jeffrey Cummings, Nick Fox, Bruno Vellas, Paul Aisen, Guogen Shan

Environmental & Global Health Faculty Research

BACKGROUND: Disease-modifying therapies are urgently needed for the treatment of Alzheimer’s disease (AD). The European Union/United States (EU/US) Task Force represents a broad range of stakeholders including biopharma industry personnel, academicians, and regulatory authorities. OBJECTIVES: The EU/US Task Force represents a community of knowledgeable individuals who can inform views of evidence supporting disease modification and the development of disease-modifying therapies (DMTs). We queried their attitudes toward clinical trial design and biomarkers in support of DMTs. DESIGN/SETTING/PARTICIANTS: A survey of members of the EU/US Alzheimer’s Disease Task Force was conducted. Ninety-three members (87%) responded. The details were analyzed to understand what …

Rock Paper Scissors And Evolutionary Game Theory, Christian Cordova, Rudolf Jovero, Evan Thomas

Math 365 Class Projects

In Rock Paper Scissors (RPS), three different "species" compete, but no single species has a dominating strategy. In evolutionary game theory, replicator equations model population densities over time. When a mutation is introduced, they are called "replicator-mutator" equations. Using the replicator-mutator equation in [1] we have shown how population density of three species change.

The Role Of Pre-Existing Type 2 Diabetes Mellitus In Colorectal Cancer Stage And Survival In Elderly Americans: A Seer-Medicare Population-Based Study 2002-~2011, Sanae El Ibrahimi

UNLV Theses, Dissertations, Professional Papers, and Capstones

Diabetes is a common comorbid condition among colorectal cancer (CRC) patients, yet its effects in CRC outcomes, particularly stage at diagnosis, risk of death and variations by diabetes severity (complications vs no complications) and Hispanic ethnicity have not been adequately studied. The purpose of this study was to investigate the association between pre-existing T2DM and advanced stage at diagnosis in elderly patients with CRC; to examine whether diabetes is an independent predictor of poor survival from all-cause and CRC-specific mortality; to assess whether variations exist by diabetes severity and to analyze the outcomes for the Hispanic group.

The Surveillance Epidemiology …

The Impact Of Economic Recession On The Health Of Adult Nevadans, Ariana Goertz

UNLV Theses, Dissertations, Professional Papers, and Capstones

Recessions are generally considered to cause negative consequences, but recent studies have provided evidence that some health outcomes improve as the economy deteriorates. The relationship between economic downfalls and health is not straightforward; it is important to look at how health has been impacted in one of the areas hit hardest by the recession. Las Vegas, Nevada was previously considered recession-proof, seemingly unaffected by previous economic downturns exhibited by the rest of the country. However, during the Great Recession of 2007-2009, Las Vegas led the country in highest rates of unemployment and foreclosures. This was quite a collapse for a …