Statistics and Probability Commons^™

Applications Of Bayesian Inference For Modelling Dynamic Instability In Neuronal Dendrite Morphogenesis, Daniel Fridman

The Yale Undergraduate Research Journal

Neurons are complex biological systems which develop intricate morphologies and whose dendrites are essential in receiving and integrating input signals from neighboring neurons. While much research has been done on the role of dendrites in neuronal development, a further understanding of dendrite dynamics can provide insight into neural development and the cellular basis of neurological diseases such as schizophrenia, Down’s syndrome, and autism. The Jonathon Howard lab hypothesizes that microtubules are a primary driving force in dendrite dynamics. Since it is known that microtubules display dynamic instability, rapidly transitioning between growth, paused, and shrinking states, the Howard lab proposes a …

Spatial Analysis Of Landscape Characteristics, Anthropogenic Factors, And Seasonality Effects On Water Quality In Portland, Oregon, Katherine Gelsey, Daniel Ramirez

REU Final Reports

Urban areas often struggle with deteriorated water quality as a result of complex interactions between landscape factors such as land cover, use, and management as well as climatic variables such as weather, precipitation, and atmospheric conditions. Green stormwater infrastructure (GSI) has been introduced as a strategy to reintroduce pre-development hydrological conditions in cities, but questions remain as to how GSI interacts with other landscape factors to affect water quality. We conducted a statistical analysis of six relevant water quality indicators in 131 water quality stations in four watersheds around Portland, Oregon using data from 2015 to 2021. Indiscriminate of station …

Modeling Covid-19 Spread In Small Colleges, Riti Bahl, Nicole Eikmeier, Alexandra Fraser, Matthew Junge, Felicia Keesing, Kukai Nakahata, Lily Reeves

Publications and Research

We develop an agent-based model on a network meant to capture features unique to COVID-19 spread through a small residential college. We find that a safe reopening requires strong policy from administrators combined with cautious behavior from students. Strong policy includes weekly screening tests with quick turnaround and halving the campus population. Cautious behavior from students means wearing facemasks, socializing less, and showing up for COVID-19 testing. We also find that comprehensive testing and facemasks are the most effective single interventions, building closures can lead to infection spikes in other areas depending on student behavior, and faster return of test …

Performance Of The Beta-Binomial Model For Clustered Binary Responses: Comparison With Generalized Estimating Equations, Seongah Im

Journal of Modern Applied Statistical Methods

This study examined performance of the beta-binomial model in comparison with GEE using clustered binary responses resulting in non-normal outcomes. Monte Carlo simulations were performed under varying intracluster correlations and sample sizes. The results showed that the beta-binomial model performed better for small sample, while GEE performed well under large sample.

Utilizing Patient-Derived Epithelial Ovarian Cancer Tumor Organoids To Predict Carboplatin Resistance, Justin W. Gorski, Zhuwei Zhang, J. Robert Mccorkle, Jodi M. Dejohn, Chi Wang, Rachel W. Miller, Holly H. Gallion, Charles S. Dietrich Iii, Frederick R. Ueland, Jill M. Kolesar

Obstetrics and Gynecology Faculty Publications

The development of patient-derived tumor organoids (TOs) from an epithelial ovarian cancer tumor obtained at the time of primary or interval debulking surgery has the potential to play an important role in precision medicine. Here, we utilized TOs to test front-line chemotherapy sensitivity and to investigate genomic drivers of carboplatin resistance. We developed six high-grade, serous epithelial ovarian cancer tumor organoid lines from tissue obtained during debulking surgery (two neoadjuvant-carboplatin-exposed and four chemo-naïve). Each organoid line was screened for sensitivity to carboplatin at four different doses (100, 10, 1, and 0.1 µM). Cell viability curves and resultant EC₅₀ values …

Chagas Disease In Hiv-Infected Patients: It’S Time To Consider The Diagnosis, Melissa Nolan Ph.D., Mph, Natasha S. Hochberg

Faculty Publications

No abstract provided.

Market Making In A Limit Order Book: Classical Optimal Control And Reinforcement Learning Approaches, Chuyi Yu

Arts & Sciences Graduate Student Theses and Dissertations

Since the last decade, algorithmic trading has become one of the most significant developments in electronic security markets. Several types of problems and practices have been studied such as optimal execution, market making, statistical arbitrage, latency arbitrage, and so on. Among these, high-frequency market making plays a crucial role since it provides large liquidity to the market, which makes trading and investing cheaper for other market participants, and also creates sizable profits for high-frequency market makers (HFM) from the large quantity of round-trip executions involved in such practices. In this thesis, we discuss two approaches to solve the high-frequency market …

Effect Of An Antenatal Lifestyle Intervention On Dietary Inflammatory Index And Its Associations With Maternal And Fetal Outcomes: A Secondary Analysis Of The Pears Trial, Sarah Louise Killen, Catherine M. Phillips, Anna Delahunt, Cara A. Yelverton, Nitin Shivappa Mbbs, Mph, Ph.D., James Hébert Scd, Maria A. Kennelly, Martina Cronin, John Mehegan, Fionnuala M. Mcauliffe

Faculty Publications

We investigated the effect of an antenatal lifestyle intervention of a low-glycaemic index (GI) diet and physical activity on energy-adjusted dietary inflammatory index (E-DIITM) and explored its relationship with maternal and child health in women with overweight and obesity. This was a secondary analysis of 434 mother−child pairs from the Pregnancy Exercise and Nutrition Study (PEARS) trial in Dublin, Ireland. E-DII^TM scores were calculated for early (10–16 weeks) and late (28 weeks) pregnancy. Outcomes included lipids, inflammation markers, insulin resistance, mode of delivery, infant size, pre-eclampsia, and gestational diabetes. T-tests were used to assess changes in E-DII^TM. …

Urinary Bile Acid Indices As Prognostic Biomarkers For The Complications Of Liver Diseases, Wenkuan Li

Theses & Dissertations

Hepatobilary diseases cause the accumulation of toxic bile acids (BA) in the liver, blood, and other tissues, which may lead to an unfavorable prognosis. In this study, we compared the urinary BA profile in 257 patients with hepatobilary diseases during a 7-year follow-up period. We investigated the use of the urinary BA profile to develop logistic regression models to predict the prognosis of hepatobiliary diseases in terms of developing disease-related complications, especially for ascites. The urinary BA profile was characterized by calculating BA indices, which quantify the composition, metabolism, hydrophilicity, and toxicity of the BA profile. All patients had high …

From Mathematics To Medicine: A Practical Primer On Topological Data Analysis (Tda) And The Development Of Related Analytic Tools For The Functional Discovery Of Latent Structure In Fmri Data, Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J. Catanzaro, Vaibhav A. Diwadkar

Mathematics Faculty Research Publications

fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. …

Empirical Fitting Of Periodically Repeating Environmental Data, Pavel Bělík, Andrew Hotchkiss, Brandon Perez, John Zobitz

Spora: A Journal of Biomathematics

We extend and generalize an approach to conduct fitting models of periodically repeating data. Our method first detrends the data from a baseline function and then fits the data to a periodic (trigonometric, polynomial, or piecewise linear) function. The polynomial and piecewise linear functions are developed from assumptions of continuity and differentiability across each time period. We apply this approach to different datasets in the environmental sciences in addition to a synthetic dataset. Overall the polynomial and piecewise linear approaches developed here performed as good (or better) compared to the trigonometric approach when evaluated using statistical measures (R^{2 …}

Modeling Reproduction Influencers Of An Endangered Oak, Camila Cortez

DePaul Discoveries

The endemic oak, Quercus brandegeei has been labeled as endangered by the IUCN Red List of Endangered Species due to its limited genetic diversity and lack of regeneration. The oak (Quercus) species is a keystone species in many parts of the world and has been facing various challenges to their survival (Westwood 2017) making efforts to support and protect endemic oaks all the more ecologically and socially imperative. There are challenges to identifying threats as there are many unknown characteristics of Q. brandegeei’s biology that are essential to carrying out conservation efforts. To develop a greater understanding of …

Sparse Domination Of The Martingale Transform, Michael Scott Kutzler

Mathematics & Statistics ETDs

Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators.

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Effect Sizes And Intra-Cluster Correlation Coefficients Measured From The Green Dot High School Study For Guiding Sample Size Calculations When Designing Future Violence Prevention Cluster Randomized Trials In School Settings, Md. Tofial Azam, Heather M. Bush, Ann L. Coker, Philip M. Westgate

Biostatistics Faculty Publications

Purpose: Cluster randomized controlled trials (cRCTs) are popular in school-based research designs where schools are randomized to different trial arms. To help guide future study planning, we provide information on anticipated effect sizes and intra-cluster correlation coefficients (ICCs), as well as school sizes, for dating violence (DV) and interpersonal violence outcomes based on data from a cRCT which evaluated the bystander-based violence intervention ‘Green Dot’.

Methods: We utilized data from 25 schools from the Green Dot High School study. Effect size and ICC values corresponding to dating and interpersonal violence outcomes are obtained from linear mixed effect models. We …

An Introduction To Calling Bullshit: Learning To Think Outside The Black Box, Jevin D. West, Carl T. Bergstrom

Numeracy

Bergstrom, Carl T. and Jevin D. West. 2020. Calling Bullshit: The Art of Skepticism in a Data-Driven World. (New York: Random House) 336 pp. ISBN 978-0525509202.

While statistical methods receive greater attention, the art of critically evaluating information in everyday life more commonly depends on thinking outside the black box of the algorithm. In this piece we introduce readers to our book and associated online teaching materials—for readers who want to more capably call “bullshit” or to teach their students to do the same.

Decision Based Learning Course Design & Implementation For Introductory Statistics, Austin Heath

Undergraduate Honors Theses

Researchers in multiple industries (biomedicine, engineering, etc.) cite the selection of an appropriate statistical test as a common problem. Experts draw on a framework of conceptual and procedural knowledge to navigate when to use statistical methods. Students also struggle determining the correct statistical method to use for a given research question. This is because they lack the opportunity to practice recognizing a host of features in each research question that provide clues for experts as to which method is most appropriate. “Decision Based Learning” (DBL) is a teaching method designed to help teachers and students address this struggle. In this …

Lapatinib And Poziotinib Overcome Abcb1-Mediated Paclitaxel Resistance In Ovarian Cancer, J. Robert Mccorkle, Justin W. Gorski, Jinpeng Liu, Mckayla J. Riggs, Anthony B. Mcdowell Jr., Nan Lin, Chi Wang, Frederick R. Ueland, Jill M. Kolesar

Markey Cancer Center Faculty Publications

Conventional frontline treatment for ovarian cancer consists of successive chemotherapy cycles of paclitaxel and platinum. Despite the initial favorable responses for most patients, chemotherapy resistance frequently leads to recurrent or refractory disease. New treatment strategies that circumvent or prevent mechanisms of resistance are needed to improve ovarian cancer therapy. We established in vitro paclitaxel-resistant ovarian cancer cell line and organoid models. Gene expression differences in resistant and sensitive lines were analyzed by RNA sequencing. We manipulated candidate genes associated with paclitaxel resistance using siRNA or small molecule inhibitors, and then screened the cells for paclitaxel sensitivity using cell viability assays. …

Associations Between Fasting Duration, Timing Of First And Last Meal, And Cardiometabolic Endpoints In The National Health And Nutrition Examination Survey, Michael David Wirth, Longgang Zhao, Gabrielle Turner-Mcgrievy, Andrew Ortaglia

Faculty Publications

Background: Research indicates potential cardiometabolic benefits of energy consumption earlier in the day. This study examined the association between fasting duration, timing of first and last meals, and cardiometabolic endpoints using data from the National Health and Nutrition Examination Survey (NHANES). Methods: Cross-sectional data from NHANES (2005–2016) were utilized. Diet was obtained from one to two 24-h dietary recalls to characterize nighttime fasting duration and timing of first and last meal. Blood samples were obtained for characterization of C-reactive protein (CRP); glycosylated hemoglobin (HbA1c %); insulin; glucose; and high-density lipoprotein (HDL), low-density lipoprotein (LDL), and total cholesterol. Survey design procedures …

Dynamics Of Plane Waves In The Fractional Nonlinear Schrödinger Equation With Long-Range Dispersion, Siwei Duo, Taras I. Lakoba, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian (−∆)α/2 . The linear stability analysis shows that plane wave solutions in the defocusing NLS are always stable if the power α ∈ [1, 2] but unstable for α ∈ (0, 1). In the focusing case, they can be linearly unstable for any α ∈ (0, 2]. We then apply the split-step Fourier spectral (SSFS) method to simulate the nonlinear stage of the plane waves dynamics. In agreement with …

Ensemble Data Fitting For Bathymetric Models Informed By Nominal Data, Samantha Zambo

Dissertations

Due to the difficulty and expense of collecting bathymetric data, modeling is the primary tool to produce detailed maps of the ocean floor. Current modeling practices typically utilize only one interpolator; the industry standard is splines-in-tension.

In this dissertation we introduce a new nominal-informed ensemble interpolator designed to improve modeling accuracy in regions of sparse data. The method is guided by a priori domain knowledge provided by artificially intelligent classifiers. We recast such geomorphological classifications, such as ‘seamount’ or ‘ridge’, as nominal data which we utilize as foundational shapes in an expanded ordinary least squares regression-based algorithm. To our knowledge …

Confluent Projections And Connectedness Of Inverse Limits, Włodzimierz J. Charatonik, Daria Michalik

Mathematics and Statistics Faculty Research & Creative Works

V. Nall proved that connectedness is preserved under inverse limits if the bounding functions are unions of functions with connected images. We show that for such functions the projections from the graph onto domain are confluent and we investigate relationships between functions satisfying this or similar conditions with confluence or openness of projections.

Housing Variables And Immigration: An Exploratory And Predictive Data Analysis In New York City, Jhonatan Medri Cobos

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The relationship between housing and immigration has become relevant in the U.S., especially in a highly populated metropolis such as New York City (NYC). Determining whether immigration status affects home ownership percentage, household rent, or housing cost percentage could help understand the quality of life of NYC residents. Graphical exploration, spatial dependence tests, and spatial autoregressive models of housing and immigration variables provide some insights about their relationships. Our exploration takes place at some geographic subareas of NYC.

Our results first indicate that the housing and immigration data reports spatial dependence; values of a geographic subarea are related to values …

Prediction Intervals: The Effects And Identification Of Sparse Regions For Nonparametric Regression Methods, Jackson Faires

Electronic Theses and Dissertations

In this work, we provide an overview of different nonparametric methods for prediction interval estimation and investigate how well they perform when making predictions in sparse regions of the predictor space. This sparsity is an extension to the more common concept of extrapolation in linear regression settings. Using simulation studies, we show that coverage probabilities using prediction intervals from quantile k-nearest neighbors and quantile random forest can be biased to low or too high from the nominal level under various situations of sparsity. We also introduce a test that can be used to see if a new data point lies …

Statistical Analysis Of Genetic Sequence Variants In Whole Exome Sequencing Data From Patients With Prostate Cancer, Kelvin Ofori-Minta

Open Access Theses & Dissertations

A single variation in the genetic sequence within the DNA of an organism could easily lead to beneficial, detrimental or neutral effects. Most often than not, these effects are detrimental than beneficial. While many biomedical and bioinformatics studies have been conducted to determine the genetic cause of prostate cancer (PrCa) which is still the second leading cause of cancer related death among men in the United States. An appreciable effort in statistical bioinformatics researches has been directed towards this aim. Through statistical analyses of a set of whole exome sequencing data from patients with PrCa obtained via The Cancer Genome …

Conditional And Marginal Imputation Models For Multilevel Data, Gang Liu

Legacy Theses & Dissertations (2009 - 2024)

This dissertation study extends sequential hierarchical regression imputation (SHRIMP) methods to multilevel datasets with three levels of nesting and proposes a marginal method based on marginalized multilevel model (MMM) framework. Specifically, the proposed model consists of two levels such that the first level relates the marginal mean of responses with covariates through a generalized regression model and the second level includes subject specific random effects within the same generalized regression model. To draw the inference on the population-averaged or subject-specified coefficients, the hierarchical regression and/or MMM is applied as the imputation and estimation models. We employ Markov Chain Monte Carlo …

Impact Of Inconsistent Imputation Models In Mediation Analysis, Bo Ye

Legacy Theses & Dissertations (2009 - 2024)

In this dissertation, we study the impact of inconsistent imputation methods in mediation analysis and its application. We present the study in three papers.

Predictive Modeling Of Clinical Outcomes For Hospitalized Covid-19 Patients Utilizing Cytof And Clinical Data., Onajia Stubblefield

Electronic Theses and Dissertations

In December 2019, an outbreak of a novel coronavirus initiated a global pandemic. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a virus that causes the disease coronavirus disease 2019 (COVID-19). Symptoms of infection with COVID-19 vary widely between individuals. While some infected individuals are asymptomatic, others need more extensive care and require hospitalization. Indeed, the COVID-19 pandemic was characterized by a shortage of hospital beds which presented additional complications in providing adequate care for patients. In this study, we used a combination of T cell population data collected from mass cytometry analysis and clinical markers to form a predictive …

Bayesian Variable Selection Strategies In Longitudinal Mixture Models And Categorical Regression Problems., Md Nazir Uddin

Electronic Theses and Dissertations

In this work, we seek to develop a variable screening and selection method for Bayesian mixture models with longitudinal data. To develop this method, we consider data from the Health and Retirement Survey (HRS) conducted by University of Michigan. Considering yearly out-of-pocket expenditures as the longitudinal response variable, we consider a Bayesian mixture model with $K$ components. The data consist of a large collection of demographic, financial, and health-related baseline characteristics, and we wish to find a subset of these that impact cluster membership. An initial mixture model without any cluster-level predictors is fit to the data through an MCMC …

Factors Influencing Student Outcomes In A Large, Online Simulation-Based Introductory Statistics Course, Ella M. Burnham

Department of Statistics: Dissertations, Theses, and Student Research

The demand for statistical knowledge and skills is growing in many disciplines, so more students are enrolling in introductory statistics courses (Blair, Kirkman, & Maxwell, 2018). At the same time, institutions are seeking course delivery methods that allow for greater flexibility for students, especially following the onset of the COVID-19 pandemic; therefore, there is more interest in the development and delivery of online introductory statistics courses.

To address this, I collaboratively designed an online introductory statistics course which focuses on simulation-based inference for the University of Nebraska-Lincoln. The course design was informed by the Community of Inquiry framework (Garrison, Anderson, …

Significant Gene Array Analysis And Cluster-Based Machine Learning For Disease Class Prediction, Myrine A. Barreiro-Arevalo

Theses and Dissertations

Gene expression analysis has been of major interest to biostatisticians for many decades. Such studies are necessary for the understanding of disease risk assessment and prediction, so that medical professionals and scientists alike may learn how to better create treatment plans to lessen symptoms and perhaps even find cures. In this study, we will investigate various gene expression analyses and machine learning techniques for disease class prediction, as well as assess predictive validity of these models and uncover differentially expressed (DE) genes for their relevant pathology datasets. Multiple gene expression datasets will be used to test model accuracies and will …