Probability Commons^™

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

Statistical Quality Control: A Bayesian Framework, Jakia Jaber Tunal

College of Graduate Studies: Theses & Dissertations

In many industries, it is important to assess whether a machine or system is operating within acceptable limits or has gone out of control. This project applies Bayesian statistics to monitor a process over time and detect changes in its behavior. First, initial data are collected to understand the system’s typical performance and to form a starting prior distribution. As new observations arrive over time, the prior is updated through Bayesian inference, combining past information with incoming data. This iterative updating creates a continuous monitoring framework that adapts as more evidence becomes available. When the updated results suggest that the …

Performance Of The Two Sample Likelihood Ratio Test Under A Nested Dirichlet: A Simulation Study, Edwina Agyeman

Electronic Theses and Dissertations

Compositional data analysis (CoDA) addresses multivariate data constrained to a constant sum, such as proportions or percentages. Originating from early warnings regarding misinterpretation by Pearson (1897), the field was formalized by John Aitchison in 1986, whose foundational work remains highly influential. Over time, new modeling techniques and visualization tools have advanced the field, as noted by Greenacre et al. More recently, Turner et al. proposed an approach based on the Nested Dirichlet Distribution (NDD), which accommodates more flexible dependence structures than the standard Dirichlet model. This thesis builds on the methodology of Turner et al. Chapter 1 introduces the nature …

Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou

LSU Doctoral Dissertations

Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …

Simulation Study On Confidence Interval Estimation For Standard Deviation With Non-Normal Distributions, Theophilus Oppong Kyeremeh

Electronic Theses and Dissertations

This study explores innovative approaches to constructing confidence intervals for the population standard deviation, σ, in non-normal data scenarios. While the sample standard deviation, s, is widely used, its reliability is compromised when dealing with skewed or heavy-tailed distributions and exhibits sensitivity to outliers. Our research addresses these limitations by investigating alternative estimation methods that offer greater robustness and accuracy.

Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov

CBN Journal of Applied Statistics (JAS)

This paper investigates the time it would take for the FTSE-100 index to reach its post-COVID-19 peak. The paper utilises an exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model that accounts for leverage effect and asymmetries. The preferred models amongst competing variants was the Autoregressive Moving Average (ARMA)-EGARCH(2,1) specification and was used to predict daily FTSE-100 data from 5th January 2000 to 21st June 2024. The empirical exercise showed that the COVID-19-induced financial crisis negatively affected the United Kingdom’s stock market performance. The results show that the FTSE100 index could reach its post-pandemic peak around 27th August, 2024 (two months after …

Uconn Baseball Reliever Lane Optimization Tool, Jason Bartholomew

Honors Scholar Theses

The building of a tool to be utilized by UConn’s Division I baseball team that will generate a game plan for when different relievers should be used against different parts of the opponent’s lineup to achieve the lowest total expected value of runs allowed for the remainder of the game based on game situations and matchup probabilities. The tool will also examine and determine situations that may be vital enough to the outcome of the game to bring in a better reliever normally saved for later in the game.

Latent Classification Of Multi-Model Non-Homogeneous Continuous-Time Markov Chains, Joonha Chang

Dissertations and Theses (Open Access)

The continuous-time Markov chain (CTMC) model and latent clustering models are commonly used to study longitudinal measures of categorical outcomes. Because of its simple but powerful Markovian property, CTMC models have been widely used in medical and public health researches. Due to limitations in the standard CTMC model, there have been some studies on non-homogeneous continuous-time Markov chain (NH-CTMC) that utilized time-dependent rates, but the progresses have been limited. NH-CTMC can be more powerful than CTMC by its default nature of time-dependent rate that can be fitted to a wider range of applications in medical studies. In this study, we …

Sensitivity Analysis Of Prior Distributions In Regression Model Estimation, Ayoade I Adewole, Oluwatoyin K. Bodunwa

Al-Bahir

Bayesian inferences depend solely on specification and accuracy of likelihoods and prior distributions of the observed data. The research delved into Bayesian estimation method of regression models to reduce the impact of some of the problems, posed by convectional method of estimating regression models, such as handling complex models, availability of small sample sizes and inclusion of background information in the estimation procedure. Posterior distributions are based on prior distributions and the data accuracy, which is the fundamental principles of Bayesian statistics to produce accurate final model estimates. Sensitivity analysis is an essential part of mathematical model validation in obtaining …

Predicting Superconducting Critical Temperature Using Regression Analysis, Roland Fiagbe

Data Science and Data Mining

This project estimates a regression model to predict the superconducting critical temperature based on variables extracted from the superconductor’s chemical formula. The regression model along with the stepwise variable selection gives a reasonable and good predictive model with a lower prediction error (MSE). Variables extracted based on atomic radius, valence, atomic mass and thermal conductivity appeared to have the most contribution to the predictive model.

Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe

Data Science and Data Mining

Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …

The Distribution Of The Significance Level, Paul O. Monnu

College of Graduate Studies: Theses & Dissertations

Reporting the p-value is customary when conducting a test of hypothesis or significance. The likelihood of getting a fictitious second sample and presuming the null hypothesis is correct is the p-value. The significance level is a statistic that interests us to investigate. Being a statistic, it has a distribution. For the F-test in a one-way ANOVA and the t-tests for population means, we define the significance level, its observed value, and the observed significance level. It is possible to derive the significance level distribution. The t-test and the F-test are not without controversy. Specifically, we demonstrate that as sample size …

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

Generalized Ratio-Product Cum Regression Variance Estimator In Two-Phase Sampling, Isah Muhammad

CBN Journal of Applied Statistics (JAS)

This study develops a flexible and efficient generalized ratio-product cum regression type estimator of population variance utilizing auxiliary variable in two-phase sampling that incorporates the properties of ratio-type and product-type estimators. The properties of the estimator were derived using first order approximation. The theoretical conditions under which the precision and the flexibility of the estimator is better than some classical estimators are also provided. Empirical evidence from five real datasets suggests that the proposed estimator outperforms the classical variance, ratio variance, product, and exponential ratio type estimators in terms of precision and efficiency. The estimator can be utilized to provide …

Improving The Efficiency Of Exponential Ratio-Type Estimator For Population Median: A Calibration Weight Adjustment Approach, Mathew J. Iseh, Kufre J. Bassey

CBN Journal of Applied Statistics (JAS)

This paper modifies the Bahl and Tuteja exponential ratio-type estimator for population median under simple random and stratified sampling schemes using calibration weight adjustment technique with supplementary information to vary the stratum weights. The bias and mean square error of the modified estimator were obtained up to the second-order approximation, which satisfies the necessary conditions for efficiency. The findings show that the new estimator surpasses existing estimators in efficiency gain. This suggests the appropriateness of calibration weight modification in boosting the efficiency of a population parameter estimator under stratified random sampling especially where the population parameter of the auxiliary variable …

Effect Of Monetary Policy Rate On Market Interest Rates In Nigeria: A Threshold And Nardl Approach, Oluwafemi E. Awopegba, Joseph O. Afolabi, Lydia T. Adeoye, Godwin O. Akpokodje

CBN Journal of Applied Statistics (JAS)

This study examines the effect of monetary policy rate (MPR) on market interest rates in Nigeria. For parsimony, we develop two indexes called the short-term interest rate (SINT) and Lending interest rate (LINT) to represent deposit and lending rates respectively. The nonlinear autoregressive distributed lag (NARDL) and threshold regression models are adopted. The study uses monthly data from 2002:M1 to 2019:M12. The results of the threshold regression model indicate that the degree of the effect of MPR on SINT and LINT above the estimated threshold of 11 and 13 percent respectively is greater and significant than if MPR were to …

Social Dimension Of Inclusive Growth In Ecowas: Implication For Poverty Reduction, Toriola K. Anu, Goerge O. Emmanuel, Ajayi O. Felix

CBN Journal of Applied Statistics (JAS)

This study investigates the implication of the social dimension of inclusive growth on poverty reduction in Economic Community of West African States (ECOWAS) countries. It specifically examines how social indices of inclusive growth comprising of income inequality, education, and health outcomes affect poverty reduction. The study uses a panel dataset of the six (6) lower-middle income countries in ECOWAS which was analysed via panel Difference Generalised Method of Moment (D-GMM). The results show that GDP per capita exerts significant negative effect on poverty while inequality, education and health outcomes do not show significant effect on poverty. Although, the estimates of …

Effect Of Fdi Inflows On Employment Generation In Selected Ecowas Countries: Heterogeneous Panel Analysis, Timothy A. Aderemi, Olawunmi Omitogun, Bukonla G. Osisanwo

CBN Journal of Applied Statistics (JAS)

The aim of this study is to examine the effect of FDI on employment in ECOWAS sub region between 1990 and 2019. The study utilizes a panel autoregressive distributed lag model to analyse the short run and long run relationship between FDI and employment across ECOWAS sub region. In the short run, the impact of FDI on employment is negative and statistically not significant. Meanwhile, in the long run FDI has a positive and statistically significant impact on employment rate. This implies that FDI has the capacity to generate employment in countries in ECOWAS sub region. Therefore, this study recommends …

Impact Of Covid-19 Pandemic On The Nigeria Stock Market: A Sectoral Stock Prices Analysis, Peter A. Adekunle, Yakubu A. Bello, Udochukwu G. Nwachukwu

CBN Journal of Applied Statistics (JAS)

This study examines the impact of the COVID-19 pandemic on sectoral stock prices in Nigeria stock market using daily data covering from February 28, 2020 to June 26, 2020. Applying the autoregressive distributed lag (ARDL) bounds test, the study finds that COVID-19 pandemic had adverse impact on the stock market indices in the short run. Furthermore, the study documents negative response of sectoral stock prices to the pandemic while the stock prices of the banking sub-sector are the worst hit. Compared to the consumer goods, and industrial subsector indices, the speed of adjustment to long run equilibrium is faster for …

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

All Dissertations

Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …

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.

On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

Arnold and Villasenor [4] obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from [4], we prove some of Arnold and Villasenor’s conjectures for samples of size three. An example with simulated data is discussed.

Personal Foul: How Head Trauma And The Insurance Industry Are Threatening Sports, Zachary Cooler

Senior Honors Theses

This thesis will investigate the growing problem of head trauma in contact sports like football, hockey, and soccer through medical studies, implications to the insurance industry, and ongoing litigation. The thesis will investigate medical studies that are finding more evidence to support the claim that contact sports players are more likely to receive head trauma symptoms such as memory loss, mood swings, and even Lou Gehrig’s disease in extreme cases. The thesis will also demonstrate that these medical symptoms and monetary losses from medical claims are convincing insurance companies to withdraw insurance coverage for sports leagues, which they are justifying …

Inferences For Weibull-Gamma Distribution In Presence Of Partially Accelerated Life Test, Mahmoud Mansour, M A W Mahmoud Prof., Rashad El-Sagheer

Basic Science Engineering

In this paper, the point at issue is to deliberate point and interval estimations for the parameters of Weibull-Gamma distribution (WGD) using progressively Type-II censored (PROG-II-C) sample under step stress partially accelerated life test (SSPALT) model. The maximum likelihood (ML), Bayes, and four parametric bootstrap methods are used to obtain the point estimations for the distribution parameters and the acceleration factor. Furthermore, the approximate confidence intervals (ACIs), four bootstrap confidence intervals and credible intervals of the estimators have been gotten. The results of Bayes estimators are computed under the squared error loss (SEL) function using Markov Chain Monte Carlo (MCMC) …

How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller

CMC Senior Theses

In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …

Statistical Inference For Networks Of High-Dimensional Point Processes, Xu Wang, Mladen Kolar, Ali Shojaie

UW Biostatistics Working Paper Series

Fueled in part by recent applications in neuroscience, high-dimensional Hawkes process have become a popular tool for modeling the network of interactions among multivariate point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work have only focused on estimation. To bridge this gap, this paper proposes a high-dimensional statistical inference procedure with theoretical guarantees for multivariate Hawkes process. Key to this inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarizes the entire history of the process. We apply this …

Generalizations Of The Arcsine Distribution, Rebecca Rasnick

Electronic Theses and Dissertations

The arcsine distribution looks at the fraction of time one player is winning in a fair coin toss game and has been studied for over a hundred years. There has been little further work on how the distribution changes when the coin tosses are not fair or when a player has already won the initial coin tosses or, equivalently, starts with a lead. This thesis will first cover a proof of the arcsine distribution. Then, we explore how the distribution changes when the coin the is unfair. Finally, we will explore the distribution when one person has won the first …

Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, Lauren Spirko-Burns, Karthik Devarajan

COBRA Preprint Series

One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease's process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous data sets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional hazards …

Non Parametric Test For Testing Exponentiality Against Exponential Better Than Used In Laplace Transform Order, Mahmoud Mansour, M A W Mahmoud Prof.

Basic Science Engineering

In this paper, the test statistic for testing exponentiality against exponential better than used in Laplace transform order (EBUL) based on the Laplace transform technique is proposed. Pitman’s asymptotic efficiency of our test is calculated and compared with other tests. The percentiles of this test are tabulated. The powers of the test are estimated for famously used distributions in aging problems. In the case of censored data, our test is applied and the percentiles are also calculated and tabulated. Finally, real examples in different areas are utilized as practical applications for the proposed test.

Counting And Coloring Sudoku Graphs, Kyle Oddson

Mathematics and Statistics Dissertations, Theses, and Final Project Papers

A sudoku puzzle is most commonly a 9 × 9 grid of 3 × 3 boxes wherein the puzzle player writes the numbers 1 - 9 with no repetition in any row, column, or box. We generalize the notion of the n² × n² sudoku grid for all n ∈ ℤ^≥2 and codify the empty sudoku board as a graph. In the main section of this paper we prove that sudoku boards and sudoku graphs exist for all such n; we prove the equivalence of [3]'s construction using unions and products of graphs to the definition of …