Probability Commons^™

A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington

Scripps Senior Theses

On May 6th, 2020, after extensive public comment and review, the Department of Education published the final rule for the new Title IX regulations, which took effect in schools on August 14th. Title IX is the nearly fifty year old piece of the Education Amendments that prohibits sexual discrimination in federally funded schools. Several of these changes, such as the inclusion of live hearings and cross examination of witnesses, have been widely criticized by victims’ rights advocates for potentially retraumatizing victims of sexual assault and discouraging students from pursuing a Title IX claim. While the impact of the new regulations …

Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis

Williams Honors College, Honors Research Projects

Concussion in sports is a prevalent medical issue. It can be difficult for medical professionals to diagnose concussions. With the fast pace nature of many sports, and the damaging effects of concussions, it is important that any concussion risks are assessed immediately. There is a growing trend of wearable technology that collects data such as steps and provides the wearer with in-depth information regarding their performance. The Smart Headband project created a wearable that can record impact data and provide the wearer with a detailed analysis on their risk of sustaining a concussion. The Smart Headband uses accelerometers and gyroscopes …

Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we …

Characterization Of Modern Ammunition And Background Profiles: A Novel Approach And Probabilistic Interpretation Of Inorganic Gunshot Residue, Korina Layli Menking-Hoggatt

Graduate Theses, Dissertations, and Problem Reports (ETD)

Gunshot residue (GSR) can provide essential clues in gun-related investigations. The standard practice for GSR analysis uses SEM-EDS, with the capability for single particle elemental and morphological analysis. However, the method is time-consuming and based on categorical classification models without considering case circumstances. Therefore, complementary and more encompassing methods are needed to improve evidence interpretation of modern ammunition. This research aims to fill these demands by developing standard materials and alternative methods to characterize and interpret IGSR.

This study developed primer GSR (pGSR) standards from sixty discharged primers that were fully characterized by three techniques. The number of GSR particles, …

Planning Algorithms Under Uncertainty For A Team Of A Uav And A Ugv For Underground Exploration, Matteo De Petrillo

Graduate Theses, Dissertations, and Problem Reports (ETD)

Robots’ autonomy has been studied for decades in different environments, but only recently, thanks to the advance in technology and interests, robots for underground exploration gained more attention. Due to the many challenges that any robot must face in such harsh environments, this remains an challenging and complex problem to solve.

As technology became cheaper and more accessible, the use of robots for underground ex- ploration increased. One of the main challenges is concerned with robot localization, which is not easily provided by any Global Navigation Services System (GNSS). Many developments have been achieved for indoor mobile ground robots, making …

Modified Firearm Discharge Residue Analysis Utilizing Advanced Analytical Techniques, Complexing Agents, And Quantum Chemical Calculations, William J. Feeney

Graduate Theses, Dissertations, and Problem Reports (ETD)

The use of gunshot residue (GSR) or firearm discharge residue (FDR) evidence faces some challenges because of instrumental and analytical limitations and the difficulties in evaluating and communicating evidentiary value. For instance, the categorization of GSR based only on elemental analysis of single, spherical particles is becoming insufficient because newer ammunition formulations produce residues with varying particle morphology and composition. Also, one common criticism about GSR practitioners is that their reports focus on the presence or absence of GSR in an item without providing an assessment of the weight of the evidence. Such reports leave the end-used with unanswered questions, …

Bayesian Techniques For Relating Genetic Polymorphisms To Diffusion Tensor Images Of Cocaine Users, Tmader Alballa

Theses and Dissertations

Past investigations utilizing Diffusion Tensor Imaging (DTI) have demonstrated that cocaine use disorder (CUD) yields white matter changes. We proposed three Bayesian techniques in order to explore the relationship between Fractional Anisotropy (FA), genetic data, and years of cocaine use (YCU). CUD participants exhibit abnormality in different areas of the brain versus non-drug using controls, which is measured by DTI. This dissertation is motivated by a neuroimaging genetic study in cocaine dependence, which found that there were relationships between several genes such as GAD and 5-HT₂R and CUD subjects.

In the first chapter, there is background on the …

Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some n ≥ 2, X1, X2, . . . , Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj ’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently …

A Brief On Optimal Transport, Austin G. Vandegriffe

Graduate Student Research & Creative Works

Optimal transport is an interesting and exciting application of measure theory to optimization and analysis. In the following, I will bring you through a detailed treatment of random variable couplings, transport plans, basic properties of transport plans, and finishing with the Wasserstein distance on spaces of probability measures with compact support. No detail is left out in this presentation, but some results have further generality and more intricate consequences when tools like measure disintegration are used. But this is left for future work.

A Brief On Characteristic Functions, Austin G. Vandegriffe

Graduate Student Research & Creative Works

Characteristic functions (CFs) are often used in problems involving convergence in distribution, independence of random variables, infinitely divisible distributions, and stochastics. The most famous use of characteristic functions is in the proof of the Central Limit Theorem, also known as the Fundamental Theorem of Statistics. Though less frequent, CFs have also been used in problems of nonparametric time series analysis and in machine learning. Moreover, CFs uniquely determine their distribution, much like the moment generating functions (MGFs), but the major difference is that CFs always exists, whereas MGFs can fail, e.g. the Cauchy distribution. This makes CFs more robust in …

Stochastic Analysis And Statistical Inference For Seir Models Of Infectious Diseases, Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Anuj Mubayi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Direct Questioning Of Sensitive Topics In Public Health Studies: A Simulation Study, Jessica K. Fox, Evrim Oral

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Controllability In Temporal Networks With Uncertainty, James C. Boerkoel Jr., Lindsay Popowski, Michael Gao, Hemeng Li, Savana Ammons, Shyan Akmal

All HMC Faculty Publications and Research

Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We provide new insights inspired by a geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability - continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods …

Video Game Genre Classification Based On Deep Learning, Yuhang Jiang

Masters Theses & Specialist Projects

Video games have played a more and more important role in our life. While the genre classification is a deeply explored research subject by leveraging the strength of deep learning, the automatic video game genre classification has drawn little attention in academia. In this study, we compiled a large dataset of 50,000 video games, consisting of the video game covers, game descriptions and the genre information. We explored three approaches for genre classification using deep learning techniques. First, we developed five image-based models utilizing pre-trained computer vision models such as MobileNet, ResNet50 and Inception, based on the game covers. Second, …

Snackjack: A Toy Model Of Blackjack, Stewart N. Ethier, Jiyeon Lee

UNLV Gaming Research & Review Journal

Snackjack is a highly simplified version of blackjack that was proposed by Ethier (2010) and given its name by Epstein (2013). The eight-card deck comprises two aces, two deuces, and four treys, with aces having value either 1 or 4, and deuces and treys having values 2 and 3, respectively. The target total is 7 (vs. 21 in blackjack), and ace-trey is a natural. The dealer stands on 6 and 7, including soft totals, and otherwise hits. The player can stand, hit, double, or split, but split pairs receive only one card per paircard (like split aces in blackjack), and …

Statistical Methods For Resolving Intratumor Heterogeneity With Single-Cell Dna Sequencing, Alexander Davis

Dissertations and Theses (Open Access)

Tumor cells have heterogeneous genotypes, which drives progression and treatment resistance. Such genetic intratumor heterogeneity plays a role in the process of clonal evolution that underlies tumor progression and treatment resistance. Single-cell DNA sequencing is a promising experimental method for studying intratumor heterogeneity, but brings unique statistical challenges in interpreting the resulting data. Researchers lack methods to determine whether sufficiently many cells have been sampled from a tumor. In addition, there are no proven computational methods for determining the ploidy of a cell, a necessary step in the determination of copy number. In this work, software for calculating probabilities from …

Uniform Random Variate Generation With The Linear Congruential Method, Joseph Free

PANDION: The Osprey Journal of Research and Ideas

This report considers the issue of using a specific linear congruential generator (LCG) to create random variates from the uniform(0,1) distribution. The LCG is used to generate multiple samples of pseudo-random numbers and statistical computation techniques are used to assess whether those samples could have resulted from a uniform(0,1) distribution. Source code is included with this report in the appendix along with annotations.

Lectures On Mathematical Computing With Python, Jay Gopalakrishnan

PDXOpen: Open Educational Resources

This open resource is a collection of class activities for use in undergraduate courses aimed at teaching mathematical computing, and computational thinking in general, using the python programming language. It was developed for a second-year course (MTH 271) revamped for a new undergraduate program in data science at Portland State University. The activities are designed to guide students' use of python modules effectively for scientific computation, data analysis, and visualization.

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Effect Of Predictor Dependence On Variable Selection For Linear And Log-Linear Regression, Apu Chandra Das

Graduate Theses and Dissertations

We propose a Bayesian approach to the Dirichlet-Multinomial (DM) regression model, which uses horseshoe, Laplace, and horseshoe plus priors for shrinkage and selection. The Dirichlet-Multinomial model can be used to find the significant association between a set of available covariates and taxa for a microbiome sample. We incorporate the covariates in a log-linear regression framework. We design a simulation study to make a comparison among the performance of the three shrinkage priors in terms of estimation accuracy and the ability to detect true signals. Our results have clearly separated the performance of the three priors and indicated that the horseshoe …

Performance Analysis Of An M/M/1 Queue With N-Policy Interrupted Closedown Preventive Maintenance Balking And Feedback, A. Azhagappan, T. Deepa

Applications and Applied Mathematics: An International Journal (AAM)

This paper investigates the transient and stationary behavior of a M/M/1 queueing model with N-policy, interrupted closedown, balking, feedback and preventive maintenance. The server stays dormant (off state) until N customers accumulate in the queue and then starts an exhaustive service (on state). After the service, each customer may either leave the system or get immediate feedback. When the system becomes empty, the server resumes closedown. If any arrival occurs before the completion of closedown time, the closedown work of the server is interrupted and starts the busy period in an exhaustive manner. If no arrival occurs during the …