Physical Sciences and Mathematics Commons^™

A New Method To Determine The Posterior Distribution Of Coefficient Alpha, John Mart V. Delosreyes

Psychology Theses & Dissertations

There is a focus within the behavioral/social sciences on non-physical, psychological constructs (i.e., constructs). These constructs are indirectly measured using measurement instruments that consist of questions that capture the manifestations of these constructs. The indirect nature of measuring constructs results in a need of ensuring that measurement instruments are reliable. The most popular statistic used to estimate reliability is coefficient alpha as it is easy to compute and has properties that make it desirable to use. Coefficient alpha’s popularity has resulted in a wide breadth of research into its qualities. Notably, research about coefficient alpha’s distribution has led to developments …

Comparing Elevator Strategies For A Parking Lot, Naveed Arafat

Major Papers

In this paper, we compare elevator strategies for a parking garage. It is assumed that the parking garage has several floors and there is an elevator which can stop on each floor. We begin by considering 4 strategies detailed in page 23. For each strategy, we loop the program 100 times, and get 100 mean values for wait times. Welch's test confirms highly significant differences among the 4 strategies. Repeating the analysis multiple times we see that the best of the 4 strategies is strategy 2, which places the elevator on floor 2 (the median floor) after use.

Identifying Advantages To Teaching Linear Regression In A Modeling And Simulation Introductory Statistics Curriculum, Kit Harris Clement

Dissertations and Theses

Statistical association is a key facet of statistical literacy: claims based on relationships between variables or ideas rooted in data are found everywhere in media and discourse. A key development in introductory statistics curricula is the use of simulation-based inference, which has shown positive outcomes for students, especially in regards to statistical literacy and conceptual understanding. In this dissertation project, I investigate students from the Change Agents for the Teaching and Learning of STatistics (CATALST) curriculum in activities I designed for learning statistical association and linear regression. First, I analyzed the informal line fitting strategies of CATALST students. Findings suggest …

Uconn Baseball Batting Order Optimization, Gavin Rublewski, Gavin Rublewski

Honors Scholar Theses

Challenging conventional wisdom is at the very core of baseball analytics. Using data and statistical analysis, the sets of rules by which coaches make decisions can be justified, or possibly refuted. One of those sets of rules relates to the construction of a batting order. Through data collection, data adjustment, the construction of a baseball simulator, and the use of a Monte Carlo Simulation, I have assessed thousands of possible batting orders to determine the roster-specific strategies that lead to optimal run production for the 2023 UConn baseball team. This paper details a repeatable process in which basic player statistics …

Statistical Approach To Quantifying Interceptability Of Interaction Scenarios For Testing Autonomous Surface Vessels, Benjamin E. Hargis, Yiannis E. Papelis

Modeling, Simulation and Visualization Student Capstone Conference

This paper presents a probabilistic approach to quantifying interceptability of an interaction scenario designed to test collision avoidance of autonomous navigation algorithms. Interceptability is one of many measures to determine the complexity or difficulty of an interaction scenario. This approach uses a combined probability model of capability and intent to create a predicted position probability map for the system under test. Then, intercept-ability is quantified by determining the overlap between the system under test probability map and the intruder’s capability model. The approach is general; however, a demonstration is provided using kinematic capability models and an odometry-based intent model.

Statistical Models For Decision-Making In Professional Soccer, Sean Hellingman

Theses and Dissertations (Comprehensive)

As soccer is widely regarded as the most popular sport in the world there is high interest in methods of improving team performances. There are many ways teams and individual athletes can influence their own performances during competition. This thesis focuses on developing statistical methodologies for improving competition-based decision-making for soccer so as to allow professional soccer teams to make better informed decisions regarding player selection and in-game decision-making.

To properly capture the dynamic actions of professional soccer, Markov chains with increasing complexity are proposed. These models allow for the inclusion of potential changes in the process caused by goals …

Comparing Voting Strategies In Blood On The Clocktower, Marty Graham

Senior Projects Spring 2023

This project models a social deduction game called “Blood on the Clocktower.” Simulated players act according to two different algorithms, and the results are recorded across four different variables. The results show that the two algorithms, while constrained to affecting one specific mechanic within the game, produce statistically different results. This model has the potential to be used in simulating group dynamics and modeling the efficacy of certain game strategies.

Stochastic Optimization To Reduce Aircraft Taxi-In Time At Igia, New Delhi, Rajib Das, Saileswar Ghosh, Rajendra Desai, Pijus Kanti Bhuin, Stuti Agarwal

International Journal of Aviation, Aeronautics, and Aerospace

Since there is an uncertainty in the arrival times of flights, pre-scheduled allocation of runways and stands and the subsequent first-come-first-served treatment results in a sub-optimal allocation of runways and stands, this is the prime reason for the unusual delays in taxi-in times at IGIA, New Delhi.

We simulated the arrival pattern of aircraft and utilized stochastic optimization to arrive at the best runway-stands allocation for a day. Optimization is done using a GRG Non-Linear algorithm in the Frontline Systems Analytic Solver platform. We applied this model to eight representative scenarios of two different days. Our results show that without …

Machine Learning Model Comparison And Arma Simulation Of Exhaled Breath Signals Classifying Covid-19 Patients, Aaron Christopher Segura

Mathematics & Statistics ETDs

This study compared the performance of machine learning models in classifying COVID-19 patients using exhaled breath signals and simulated datasets. Ground truth classification was determined by the gold standard Polymerase Chain Reaction (PCR) test results. A residual bootstrapped method generated the simulated datasets by fitting signal data to Autoregressive Moving Average (ARMA) models. Classification models included neural networks, k-nearest neighbors, naïve Bayes, random forest, and support vector machines. A Recursive Feature Elimination (RFE) study was performed to determine if reducing signal features would improve the classification models performance using Gini Importance scoring for the two classes. The top 25% of …

(R1239) A New Type Ii Half Logistic-G Family Of Distributions With Properties, Regression Models, System Reliability And Applications, Emrah Altun, Morad Alizadeh, Haitham M. Yousof, Mahdi Rasekhi, G. G. Hamedani

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a new family of distributions based on the half logistic distribution. With the new family, the baseline distributions gain flexibility through additional shape parameters. The important statistical properties of the proposed family are derived. A new generalization of the Weibull distribution is used to introduce a location-scale regression model for the censored response variable. The utility of the introduced models is demonstrated in survival analysis and estimation of the system reliability. Three data sets are analyzed. According to the empirical results, it is observed that the proposed family gives better results than other existing models.

Compound Sums, Their Distributions, And Actuarial Pricing, Ang Li

Electronic Thesis and Dissertation Repository

Compound risk models are widely used in insurance companies to mathematically describe their aggregate amount of losses during certain time period. However, evaluation of the distribution of compound random variables and the computation of the relevant risk measures are non-trivial. Therefore, the main purpose of this thesis is to study the bounds and simulation methods for both univariate and multivariate compound distributions. The premium setting principles related to dependent multivariate compound distributions are studied. .

In the first part of this thesis, we consider the upper and lower bounds of the tail of bivariate compound distributions. Our results extend those …

Applying Deep Learning To The Ice Cream Vendor Problem: An Extension Of The Newsvendor Problem, Gaffar Solihu

Electronic Theses and Dissertations

The Newsvendor problem is a classical supply chain problem used to develop strategies for inventory optimization. The goal of the newsvendor problem is to predict the optimal order quantity of a product to meet an uncertain demand in the future, given that the demand distribution itself is known. The Ice Cream Vendor Problem extends the classical newsvendor problem to an uncertain demand with unknown distribution, albeit a distribution that is known to depend on exogenous features. The goal is thus to estimate the order quantity that minimizes the total cost when demand does not follow any known statistical distribution. The …

On The Estimation Of Heston-Nandi Garch Using Returns And/Or Options: A Simulation-Based Approach, Xize Ye

Electronic Thesis and Dissertation Repository

In this thesis, the Heston-Nandi GARCH(1,1) (henceforth, HN-GARCH) option pricing model is fitted via 4 maximum likelihood-based estimation and calibration approaches using simulated returns and/or options. The purpose is to examine the benefits of the joint estimation using both returns and options over the fundamental returns-only estimation on GARCH models. From our empirical studies, with the additional option sample, we can improve the efficiency of the estimates for HN-GARCH parameters. Nonetheless, the improvements for the risk premium factor, both from empirical standard errors, and sample RMSEs, are insignificant. In addition, option prices are simulated with a pre-defined noise structure and …

Jmasm 57: Bayesian Survival Analysis Of Lomax Family Models With Stan (R), Mohammed H. A. Abujarad, Athar Ali Khan

Journal of Modern Applied Statistical Methods

An attempt is made to fit three distributions, the Lomax, exponential Lomax, and Weibull Lomax to implement Bayesian methods to analyze Myeloma patients using Stan. This model is applied to a real survival censored data so that all the concepts and computations will be around the same data. A code was developed and improved to implement censored mechanism throughout using rstan. Furthermore, parallel simulation tools are also implemented with an extensive use of rstan.

Observational Studies In Group Testing And Potential Applications., Alexander Christopher Noll

Electronic Theses and Dissertations

The use of group testing to identify individuals with targeted outcomes in a population can greatly improve the efficiency, speed, and cost effectiveness of testing a population for an outcome, or at least for identifying the prevalence of an outcome in a population. The implementation of causal inference techniques can provide the basis for an observational study that would allow an investigator to gather estimates for treatment effectiveness if group testing was conducted on the population in a certain way. This thesis examines a simulation of the above outlined principles in order to demonstrate a potential application for determining treatment …

The Wargaming Commodity Course Of Action Automated Analysis Method, William T. Deberry

Theses and Dissertations

This research presents the Wargaming Commodity Course of Action Automated Analysis Method (WCCAAM), a novel approach to assist wargame commanders in developing and analyzing courses of action (COAs) through semi-automation of the Military Decision Making Process (MDMP). MDMP is a seven-step iterative method that commanders and mission partners follow to build an operational course of action to achieve strategic objectives. MDMP requires time, resources, and coordination – all competing items the commander weighs to make the optimal decision. WCCAAM receives the MDMP's Mission Analysis phase as input, converts the wargame into a directed graph, processes a multi-commodity flow algorithm on …

The Simulation Extrapolation Method With Differential Measurement Error, Dominic Partipilo

Graduate Research Theses & Dissertations

Most of statistical theory operates under the assumption that the true values of covariates have been measured correctly, but it is not always possible to obtain the true values of these covariates. A common issue, specifically in regression models, is that predictors are misclassified or measured with systematic measurement error. There have been many methods developed for handling measurement error, specifically in the case where measurement error is nondifferential, where the measurement error can be treated as independent from the covariates. The frequentist method known as simulation extrapolation (SIMEX) is one of these methods that specifically handles the case for …

The Odd Inverse Rayleigh Family Of Distributions: Simulation & Application To Real Data, Saeed E. Hemeda, Muhammad A. Ul Haq

Applications and Applied Mathematics: An International Journal (AAM)

A new family of inverse probability distributions named inverse Rayleigh family is introduced to generate many continuous distributions. The shapes of probability density and hazard rate functions are investigated. Some Statistical measures of the new generator including moments, quantile and generating functions, entropy measures and order statistics are derived. The Estimation of the model parameters is performed by the maximum likelihood estimation method. Furthermore, a simulation study is used to estimate the parameters of one of the members of the new family. The data application shows that the new family models can be useful to provide better fits than other …

Interval Estimation Of Proportion Of Second-Level Variance In Multi-Level Modeling, Steven Svoboda

The Nebraska Educator: A Student-Led Journal

Physical, behavioral and psychological research questions often relate to hierarchical data systems. Examples of hierarchical data systems include repeated measures of students nested within classrooms, nested within schools and employees nested within supervisors, nested within organizations. Applied researchers studying hierarchical data structures should have an estimate of the intraclass correlation coefficient (ICC) for every nested level in their analyses because ignoring even relatively small amounts of interdependence is known to inflate Type I error rate in single-level models. Traditionally, researchers rely upon the ICC as a point estimate of the amount of interdependency in their data. Recent methods utilizing an …

Can Auxiliary Information Improve Rasch Estimation At Small Sample Sizes?, Derek Sauder

Dissertations, 2020-current

The Rasch model is commonly used to calibrate multiple choice items. However, the sample sizes needed to estimate the Rasch model can be difficult to attain (e.g., consider a small testing company trying to pretest new items). With small sample sizes, auxiliary information besides the item responses may improve estimation of the item parameters. The purpose of this study was to determine if incorporating item property information (i.e., characteristics of the items related to item difficulty) in a random effects linear logistic test model (RE-LLTM) would improve estimation of item difficulty. A simulation study was conducted that varied sample size, …

Propensity Score Matching And Generalized Boosted Modeling In The Context Of Model Misspecification: A Simulation Study, Briana G. Craig

Masters Theses, 2020-current

In the absence of random assignment, researchers must consider the impact of selection bias – pre-existing covariate differences between groups due to differences among those entering into treatment and those otherwise unable to participate. Propensity score matching (PSM) and generalized boosted modeling (GBM) are two quasi-experimental pre-processing methods that strive to reduce the impact of selection bias before analyzing a treatment effect. PSM and GBM both examine a treatment and comparison group and either match or weight members of those groups to create new, balanced groups. The new, balanced groups theoretically can then be used as a proxy for the …

Dot: Gene-Set Analysis By Combining Decorrelated Association Statistics, Olga A. Vsevolozhskaya, Min Shi, Fengjiao Hu, Dmitri V. Zaykin

Biostatistics Faculty Publications

Historically, the majority of statistical association methods have been designed assuming availability of SNP-level information. However, modern genetic and sequencing data present new challenges to access and sharing of genotype-phenotype datasets, including cost of management, difficulties in consolidation of records across research groups, etc. These issues make methods based on SNP-level summary statistics particularly appealing. The most common form of combining statistics is a sum of SNP-level squared scores, possibly weighted, as in burden tests for rare variants. The overall significance of the resulting statistic is evaluated using its distribution under the null hypothesis. Here, we demonstrate that this basic …

Assessing Robustness Of The Rasch Mixture Model To Detect Differential Item Functioning - A Monte Carlo Simulation Study, Jinjin Huang

Electronic Theses and Dissertations

Measurement invariance is crucial for an effective and valid measure of a construct. Invariance holds when the latent trait varies consistently across subgroups; in other words, the mean differences among subgroups are only due to true latent ability differences. Differential item functioning (DIF) occurs when measurement invariance is violated. There are two kinds of traditional tools for DIF detection: non-parametric methods and parametric methods. Mantel Haenszel (MH), SIBTEST, and standardization are examples of non-parametric DIF detection methods. The majority of parametric DIF detection methods are item response theory (IRT) based. Both non-parametric methods and parametric methods compare differences among subgroups …

Paper Structure Formation Simulation, Tyler R. Seekins

Electronic Theses and Dissertations

On the surface, paper appears simple, but closer inspection yields a rich collection of chaotic dynamics and random variables. Predictive simulation of paper product properties is desirable for screening candidate experiments and optimizing recipes but existing models are inadequate for practical use. We present a novel structure simulation and generation system designed to narrow the gap between mathematical model and practical prediction. Realistic inputs to the system are preserved as randomly distributed variables. Rapid fiber placement (~1 second/fiber) is achieved with probabilistic approximation of chaotic fluid dynamics and minimization of potential energy to determine flexible fiber conformations. Resulting digital packed …

Spatio-Temporal Cluster Detection And Local Moran Statistics Of Point Processes, Jennifer L. Matthews

Mathematics & Statistics Theses & Dissertations

Moran's index is a statistic that measures spatial dependence, quantifying the degree of dispersion or clustering of point processes and events in some location/area. Recognizing that a single Moran's index may not give a sufficient summary of the spatial autocorrelation measure, a local indicator of spatial association (LISA) has gained popularity. Accordingly, we propose extending LISAs to time after partitioning the area and computing a Moran-type statistic for each subarea. Patterns between the local neighbors are unveiled that would not otherwise be apparent. We consider the measures of Moran statistics while incorporating a time factor under simulated multilevel Palm distribution, …

Jmasm 51: Bayesian Reliability Analysis Of Binomial Model – Application To Success/Failure Data, M. Tanwir Akhtar, Athar Ali Khan

Journal of Modern Applied Statistical Methods

Reliability data are generated in the form of success/failure. An attempt was made to model such type of data using binomial distribution in the Bayesian paradigm. For fitting the Bayesian model both analytic and simulation techniques are used. Laplace approximation was implemented for approximating posterior densities of the model parameters. Parallel simulation tools were implemented with an extensive use of R and JAGS. R and JAGS code are developed and provided. Real data sets are used for the purpose of illustration.

Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick

Theses, Dissertations and Capstones

In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S ² ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, V^ˆ (S ² ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.

Comparing Performance Of Gene Set Test Methods Using Biologically Relevant Simulated Data, Richard M. Lambert

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Today we know that there are many genetically driven diseases and health conditions. These problems often manifest only when a set of genes are either active or inactive. Recent technology allows us to measure the activity level of genes in cells, which we call gene expression. It is of great interest to society to be able to statistically compare the gene expression of a large number of genes between two or more groups. For example, we may want to compare the gene expression of a group of cancer patients with a group of non-cancer patients to better understand the genetic …

Predictions Generated From A Simulation Engine For Gene Expression Micro-Arrays For Use In Research Laboratories, Gopinath R. Mavankal, John Blevins, Dominique Edwards, Monnie Mcgee, Andrew Hardin

SMU Data Science Review

In this paper we introduce the technical components, the biology and data science involved in the use of microarray technology in biological and clinical research. We discuss how laborious experimental protocols involved in obtaining this data used in laboratories could benefit from using simulations of the data. We discuss the approach used in the simulation engine from [7]. We use this simulation engine to generate a prediction tool in Power BI, a Microsoft, business intelligence tool for analytics and data visualization [22]. This tool could be used in any laboratory using micro-arrays to improve experimental design by comparing how predicted …

Estimation Of The Burr Xii-Exponential Distribution Parameters, Gholamhossein Yari, Zahra Tondpour

Applications and Applied Mathematics: An International Journal (AAM)

The Burr XII distribution is one of the most important distributions in Survival analysis. In this article, we introduce the new wider Burr XII-G family of distributions. A special model in the new family called Burr XII-exponential distribution that has constant, decreasing and unimodal hazard rate functions is investigated. We discuss the estimation of this distribution parameters by maximum likelihood, three modifications of maximum likelihood and Bayes methods. In Bayes method, we use the uniform, triangular and Burr XII-uniform priors for posterior analysis and obtain Bayes estimations under two different loss functions. We obtain two approximations of the Bayes estimations, …