Statistics and Probability Commons^™

Anticipating Stochastic Integrals And Related Linear Stochastic Differential Equations, Sudip Sinha

LSU Doctoral Dissertations

Itô’s stochastic calculus revolutionized the field of stochastic analysis and has found numerous applications in a wide variety of disciplines. Itô’s theory, even though quite general, cannot handle anticipating stochastic processes as integrands. There have been considerable efforts within the mathematical community to extend Itô’s calculus to account for anticipation. The Ayed–Kuo integral — introduced in 2008 — is one of the most recent developments. It is arguably the most accessible among the theories extending Itô’s calculus — relying solely on probabilistic methods. In this dissertation, we look at the recent advances in this area, highlighting our contributions. First, we …

Machine Learning In Support Of Student Success, Rachel Rucker

Undergraduate Research Conference

Our goal is to predict whether a student will finish the semester on academic probation by mid-term using university data.

Indian Statistical Institute Placement Brochure 2021-2022, Indian Statistical Institute

Poster and Presentations

The Placement Cell at the ISI Delhi Centre presents a comprehensive information brochure detailing the placement opportunities for outgoing students during 2021–2022. It outlines the placement process for M.Stat and MS-QE students at ISI Delhi. Respective companies should inform the Placement Committee of the final selected candidates, preferably within a day or two.

Molecular Characterization Of Rickettsial Agents In Ticks (Acari: Ixodidae) From Sri Lanka, Gregory A. Dasch, Marina Eremeeva, Maria L. Zambrano, Ranjan Premaratna, S. A. M. Kularatne

Biostatistics, Epidemiology & Environmental Health Sciences: Faculty Publications

Because the majority of spotted fever group rickettsiae are transmitted to humans by tick bites, it is important to understand which ticks might play a role in transmission of rickettsial pathogens in Sri Lanka. The purpose of our study was to conduct molecular surveillance of 847 ticks collected in different locations in central Sri Lanka to determine which were infected with Rickettsia and Anaplasmataceae. Molecular methods were used to identify the ticks and the agents detected. Most ticks (Amblyomma, Haemaphysalis, and Rhipicephalus) were collected by flagging, and lower number was collected from dogs, cattle, pigs, a …

Eigenfunction Restriction Estimates For Curves With Nonvanishing Geodesic Curvatures In Compact Riemannian Surfaces With Nonpositive Sectional Curvatures, Chamsol Park

Mathematics & Statistics ETDs

For 2 ≤ p < 4, we study the Lp norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact 2-dimensional Riemannian manifolds. Burq, G\´erard, and Tzvetkov [12], and Hu [21] found eigenfunction restriction estimates for a curve with nonvanishing geodesic curvatures. We will explain how the proof of the known estimates helps us to consider the case where the given smooth compact Riemannian manifold has nonpositive sectional curvatures. For p = 4, we will also obtain a logarithmic analogous estimate, by using arguments in Xi and Zhang [37], Sogge [33], and Bourgain [10]. At the end of this dissertation, we will talk about a future work, which is a follow up study for higher dimensional analogues of the above curve cases.

White Noise Space Analysis And Multiplicative Change Of Measures, Daniel Alpay, Palle Jorgensen, Motke Porat

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a corresponding family of representations of the canonical commutation relations (CCR) in an infinite number of degrees of freedom. A key feature of our construction is explicit formulas for associated transforms; these are infinite-dimensional analogs of Fourier transforms. Our framework is that of Gaussian Hilbert spaces, reproducing kernel Hilbert spaces and Fock spaces. The latter forms the setting for our …

General Stochastic Calculus And Applications, Pujan Shrestha

LSU Doctoral Dissertations

In 1942, K. Itô published his pioneering paper on stochastic integration with respect to Brownian motion. This work led to the framework for Itô calculus. Note that, Itô calculus is limited in working with knowledge from the future. There have been many generalizations of the stochastic integral in being able to do so. In 2008, W. Ayed and H.-H. Kuo introduced a new stochastic integral by splitting the integrand into the adaptive part and the counterpart called instantly independent. In this doctoral work, we conduct deeper research into the Ayed–Kuo stochastic integral and corresponding anticipating stochastic calculus.

We provide a …

Pro-Inflammatory Diet Pictured In Children With Atopic Dermatitis Or Food Allergy: Nutritional Data Of The Lina Cohort, Olivia Schütte, Larissa Bachmann, Nitin Shivappa Mbbs, Mph, Ph.D., James R. Hébert Scd, Janine F. Felix, Stefan Röder, Ulrich Sack, Michaek Borte, Wieland Kiess, Ana C. Zenclussen, Gabriele I. Stangl

Faculty Publications

Background: Lifestyle and environmental factors are known to contribute to allergic disease development, especially very early in life. However, the link between diet composition and allergic outcomes remains unclear. Methods: In the present population-based cohort study we evaluated the dietary intake of 10-year-old children and analyses were performed with particular focus on atopic dermatitis or food allergy, allergic diseases known to be affected by dietary allergens. Dietary intake was assessed via semi-quantitative food frequency questionnaires. Based on these data, individual nutrient intake as well as children’s Dietary Inflammatory Index (C-DII™) scores were calculated. Information about atopic manifestations during the first …

Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano

Electrical and Computer Engineering ETDs

Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …

Dietetic Intervention In Psoriatic Arthritis: The Dieta Trial, Beatriz F. Leite, Melissa A. Morimoto, Carina M. F. Gomes, Barbara N.C. Klemz, Patrícia S. Genaro, Nitin Shivappa Mbbs, Mph, Ph.D., James R. Hébert Scd, Nágila R.T. Damasceno, Marcelo M. Pinheiro

Faculty Publications

Aim To evaluate whether dietary pattern changes, antioxidant supplementation or 5-10% weight loss could improve disease activity (skin and joint) in patients with psoriatic arthritis (PsA). Methods A total of 97 PsA patients were enrolled in this 12-week randomized, double-blinded, placebo-controlled trial. Patients were randomized into three groups: Diet-placebo (hypocaloric diet + placebo supplementation); Diet-fish (hypocaloric diet + 3 g/day of omega-3 supplementation; and Placebo. Food intake (3-day registry, Healthy Eating Index (HEI), and the Dietary Inflammatory Index (DII)), body composition (whole-body dual-energy X-ray absorptiometry (DXA), weight and waist circumference) and disease activity (PASI, BSA, BASDAI, DAS28-ESR, DAS28-CRP and MDA) …

Factors That Influence Graduation Rates At Northwestern College, Hailey Louw, Jennifer Schon

Celebration of Research

This project examines factors that influence graduation rates regarding behaviors and choices made in college as opposed to exogenous factors such as family income, race, etc. These factors also included responses from first-year students who took the Cooperative Institutional Research Program (CIRP) survey. Using data from 2013 - 2016 freshman admissions and combining this with CIRP responses from 2014 and 2016, there were found to be five factors related to behavior at college that influenced graduation rates.

Completion of registered hours, campus involvement, and high tuition discount rates had strong, positive correlations with whether the student graduated. Student participation in …

Predicting Student Graduation At A Private College, Theo Jongerius, Jennifer Schon

Celebration of Research

The purpose of this project was to accurately predict which students attending Northwestern will graduate based on information we collect on incoming students, as well as information we gain from students during their time at NWC.

Through use of the programming language Python and its machine learning libraries, I was able to develop a machine learning model that can accurately predict if a student would graduate 85% of the time.

Women Enrollment At Northwestern College, Josiah Bonestroo, Jennifer Schon

Celebration of Research

This project observes the enrollment rate of women at Northwestern College and why it is inconsistent. Data is used from satisfaction surveys of 2020 and 2021 enrollees, with the data being analyzed using R Studio. Types of data observed include type of visits students went on, types of scholarships, and interest in a Christian college atmosphere.

Relationship Between Higher Education And Health Insurance Coverage And Healthcare Utilization For Black Or African American Individuals, Emma Revoir

Psychology Student Works

Higher education may decrease mortality due to higher income and health insurance availability (Buckles et al., 2016). Education can increase understanding and utilizing health insurance (Gallo et al., 2020). There is a gap in how this relationship affects racial minorities. This study aims to understand how health insurance is affected by education level for Black or African American individuals.

The Association Between Sibling Relationships And Personality, Rebecca Ramsey

Psychology Student Works

Differences in self perception (specifically aggression) was discovered in participants with siblings, and no difference of intelligence, outgoing personalities, creativity, competitiveness and family orientation (Van Volkom, Guerguis, & Kramer, 2017). Sisters were found to have more empathy than the brothers along with higher intimacy, knowledge, and emotional support (Walęcka-Matyja, 2017). There is a gap in my research between sibling jealousy and depression, sibling negativity, and intimacy in young adulthood (Hamwey & Whiteman, 2020). My study examines the similarity of personality to siblings. Some personality traits may include jealousy, outgoingness, competitiveness, and creativity.

How Quality Of Paternal Relationship Impacts Depression Development In Adulthood, Rachel Lane

Psychology Student Works

Previous studies show that paternal involvement directly correlates to a decrease in the child’s probability of developing a mental illness (O’Gara, et.al. 2019). Research shows, the more supportive and the more affection a parent gives, the less likely a child is to develop depressive tendencies (Del Barrio, et. al. 2016) There is a gap in investigating whether or not having a loving father postpones the age at which someone is diagnosed with depression. This study provides insight into paternal closeness and the age at which someone is diagnosed with depression.

The Association Between Promiscuity And Marital Satisfaction, Shelby Kate Christopher

Psychology Student Works

Research has suggested that premarital cohabitation is linked to a heightened risk of divorce and dissatisfaction if it occurs with someone other than the marriage partner (Teachman, 2004). The number of partners is linked to marital dissatisfaction for both men and women (Legkauskas & Stankevičienė, 2008). Involvement in church groups is linked to a 5x increase in likelihood of abstinence (Paul et al, 2000). Previous studies have used small sample sizes with little diversity and few men. However, my research will use a large, diverse sample size with both men and women.

The Association Between Religiosity And Alcohol Use In Adolescents, Daphny Vang

Psychology Student Works

Research has found that the age and strength of religion directly correlate to the level of alcohol consumption(Mason & Windle, 2002). Previous studies show that adult women with stronger religious beliefs consume less alcohol compared to those with weaker religious beliefs (Mattila & et al., 2001). There is a gap in investigating the relationship between religiosity and alcohol use in adolescents. This study provides insight into the relationship between religiosity and alcohol consumption with adolescents.

The Relationship Between Adults Education Level And Their Mental Health Status, Kelsey Bergan

Psychology Student Works

Research has shown that those with a higher education are more likely to seek out sources to help them with mental disorders (Ibrahim, et al., 2019; Neimeyer, et al., 2011). Previous studies have found that students with a lower GPA show signs of depression, anxiety and eating disorders (Eisenberg, Globerstein & Hunt, 2009). There is a gap in investigating the relationship between education level and an adult’s mental health experiences. This study will provide insight to the relationship between an adults education level and their mental health.

The Relationship Between Adolescents’ Participation In Religious/Spiritual Activities And Mental Health As An Adult, Tiara Lamb

Psychology Student Works

Many receiving mental health treatment across the U.S. see spirituality and religion as very helpful in supporting their mental state (Oxhandler et al., 2021). How often black Americans attended church in adolescence is related to how as a young adult they could spiritually handle mentally stressing situations (Alexander, 2017). There’s a gap in previous studies because most of them study specific groups rather than using a representative sample of the U.S. In addition, there is a lack of studies investigating the relationship between adolescent religiosity/spirituality and adult mental health. This study uses a representative sample and investigates the association between …

The Association Of Maternal Relationships And Acts Of Violence In Adults, Cameron Shores

Psychology Student Works

Through research it has been found that people who do not feel close to their parents are more likely to react with violence (Cano-Lozano et al., 2020). Studies have also shown that people who reported adverse relationships as children, tend to have more violence-related outcomes (Duke, 2010). There is currently a gap in explaining the association between maternal closeness and violent tendencies. This study is meant to help fill that gap and bring cognizance to the relationship between maternal closeness and violence.

Empirically Adjusted Weighted Ordered P-Values Method, Wimarsha Jayanetti, Sinjini Sikdar, N. Rao Chaganty

College of Sciences Posters

Recent advancements in high-throughput technologies have enabled simultaneous inference of thousands of genes. With the abundance of public databases, it is now possible to rapidly access the results of several genomic studies, each of which includes the significance testing results of a large number of genes. Researchers frequently aggregate genomic data from multiple studies in the form of a meta-analysis. Most traditional meta-analysis methods aim at combining summary results to find signals in at least one of the studies. However, often the goal is to identify genes that are differentially expressed in a consistent pattern across multiple studies. Recently, a …

Hypothesis Testing Of Student's Mathematical Performance In Relation To The Covid-19 Pandemic, Elizabeth Foster

Mathematics Senior Capstone Papers

The COVID-19 Pandemic affected everyone, especially schools and education due to the rapid switch from traditional face-to-face classes to online and hybrid classes. The goal of this study is to see how the pandemic affected students’ grades during distance learning when compared to before. Using hypothesis testing, we will analyze data from 13 sections of MATH 243 classes to determine if the averages went down during the pandemic, specifically in hybrid class settings. Based on the raw data of the test grades in relation to the COVID-19 Pandemic, a significant difference can be found in test scores before and during …

Factors That Relate To Academic Excellence, Matthew Lemoine

Mathematics Senior Capstone Papers

The American College Testing (ACT) provides university admissions offices a look into a student’s academic ability so that the university can determine admittance and scholarships. The premise of this study is to see whether this is the most effective way to determine academic ability, using the Logistic Regression Model. The data was collected from October 21, 2021 to December 31, 2021 at Louisiana Tech University. Using the Logistic Regression Model, predictions of academic excellence are obtained based on the parameters outlined in this paper. After the parameters for the Logistic Regression Model are calculated, conclusions can be drawn that the …

Statistical Analysis Of Home-Field Advantage In European Soccer, Francisco Simoncini

Mathematics Senior Capstone Papers

Home-field advantage in the sports world is commonly known as a huge factor in determining the final score of any sports game. By using a one-tailed, two-sample t-test, I am analyzing how playing at home generally affects a European soccer team’s performance. I am looking at how these performances are affected across three domestic leagues in Europe. I predict that when teams play at home, there will be a significant difference in their win ratio and goals scored.

Flood Risk Prediction In Southern Louisiana Using Support Vector Machines, Claire Dorsett

Mathematics Senior Capstone Papers

Flooding in Southern Louisiana is a growing concern as violent weather becomes more frequent. According to the Environmental Protection Agency (EPA), Louisiana soils have become drier and annual rainfall trends have increased, which may lead to more severe flooding in the coming years. In light of this change in weather trends, flood prediction has become increasingly important for the public’s safety. The focus of this paper is to apply the Support Vector Machine (SVM), a machine learning technique, to classify flood risks based on water gage height, wind speed and direction, and time of the year. In this paper, the …

A Monte Carlo Analysis Of Seven Dichotomous Variable Confidence Interval Equations, Morgan Juanita Dubose

Masters Theses & Specialist Projects

Department of Psychological Sciences Western Kentucky University There are two options to estimate a range of likely values for the population mean of a continuous variable: one for when the population standard deviation is known and another for when the population standard deviation is unknown. There are seven proposed equations to calculate the confidence interval for the population mean of a dichotomous variable: normal approximation interval, Wilson interval, Jeffreys interval, Clopper-Pearson, Agresti-Coull, arcsine transformation, and logit transformation. In this study, I compared the percent effectiveness of each equation using a Monte Carlo analysis and the interval range over a range …

A New Application Of The Central Limit Theorem, Kenneth Winters

Selected Honors Theses

This paper discusses the Central Limit Theorem (CLT) and its applications. The paper gives an introduction to what the CLT is and how it can be applied to real life. Additionally, the paper gives a conceptual understanding of the theorem through various examples and visuals. The paper discusses the applications of the CLT in fields such as computer science, psychology, and political science. The author then suggests a new mathematical theorem as an application of the CLT and provides a proof of the theorem. The new theorem relates to expected value and probabilities of random variables and provides a link …

Math 672: Statistical Methods Ii, Dao Nguyen

GMAS Course Syllabi

No abstract provided.

Math 777: Seminar In Statistics: Theoretical Foundations Of Neural Network Learning, Instructor: Hailin Sang

GMAS Course Syllabi

No abstract provided.