Physical Sciences and Mathematics Commons^™

Parameter Estimation For Patient Enrollment In Clinical Trials, Junyan Liu

Undergraduate Honors Theses

In this paper, we study the Poisson-gamma model for recruitment time in clinical trials. We proved several properties of this model that match our intuitions from a reliability perspective, did simulations on this model, and used different optimization methods to estimate the parameters. Although the behaviors of the optimization methods were unfavorable and unstable, we identified certain conditions and provided potential explanations for this phenomenon and further insights into the Poisson-gamma model.

Statistical Modeling: Regression, Survival Analysis, And Time Series Analysis, Lawrence Leemis

Open Education Resources (OER)

Statistical Modeling provides an introduction to regression, survival analysis, and time series analysis for students who have completed calculus-based courses in probability and mathematical statistics. The book uses the R language to fit statistical models, conduct Monte Carlo simulation experiments and generate graphics. Over 300 exercises at the end of the chapters makes this an appropriate text for a class in statistical modeling.

Part 1: Regression
Chapter 1: Simple Linear Regression
Chapter 2: Inference in Simple Linear Regression
Chapter 3: Topics in Regression

Part II: Survival Analysis
Chapter 4: Probability Models in Survival Analysis
Chapter 5: Statistical Methods in Survival …

The Probability Mass Function Of The Kaplan-Meier Product-Limit Estimator, Yuxin Qin, Heather Sasinowska, Lawrence Leemis

Arts & Sciences Articles

Kaplan andMeier’s 1958 article developed a nonparametric estimator of the survivor function from a right censored dataset. Determining the size of the support of the estimator as a function of the sample size provides a challenging exercise for students in an advanced course in mathematical statistics. We devise two algorithms for calculating the support size and calculate the associated probability mass function for small sample sizes and particular probability distributions for the failure and censoring times.

Bayesian Spatial Model Development Of Soil Core Organic Matter As A Proxy For Blue Carbon Stocks Within The Chesapeake Bay, Christian Longo

Undergraduate Honors Theses

Blue carbon is carbon captured and stored within bodies of water and their ecosystems. Blue carbon stocks are very important due to their ability to store carbon away from the atmosphere. The destruction of these stocks can accelerate climate change. In particular, we wish to assess blue carbon stock within the Chesapeake Bay. Previous studies have only used geographical features to predict blue carbon stock levels. The big picture question this thesis was meant to answer is: What is the best approach for building a statistical model that factors in both spatial parameters and geographical features to predict blue carbon …

Period Doubling Cascades From Data, Alexander Berliner

Undergraduate Honors Theses

Orbit diagrams of period doubling cascades represent systems going from periodicity to chaos. Here, we investigate whether a Gaussian process regression can be used to approximate a system from data and recover asymptotic dynamics in the orbit diagrams for period doubling cascades. To compare the orbits of a system to the approximation, we compute the Wasserstein metric between the point clouds of their obits for varying bifurcation parameter values. Visually comparing the period doubling cascades, we note that the exact bifurcation values may shift, which is confirmed in the plots of the Wasserstein distance. This has implications for studying dynamics …

Using Machine Learning To Track The Location Of The Shock Train In Hypersonic Engines, Alison Reynolds

Undergraduate Honors Theses

Proposed hypersonic vehicles would be able to travel at five to ten times the speed of sound, but there are still many problems that need to be solved to construct a functioning vehicle. One such problem involves shocks created in the engine isolator when the vehicle reaches high speeds. These shocks must be contained to the isolator to maximize performance and avoid potential failure. This project attempts to track the location of the leading shock given images of airflow from ground tests of engines using random forests and convolutional neural networks. When the models are trained and tested on data …

Random Sampling, Lawrence Leemis

Arts & Sciences Book Chapters

Mathematical Statistics describes the mathematical underpinnings associated with the practice of statistics. The pre-requisite for this book is a calculus-based course in probability. Nearly 200 figures and dozens of Monte Carlo simulation experiments in R help develop the intuition behind the statistical methods. Real-world problems from a wide range of fields help the reader apply the statistical methods. Over 300 exercises are used to reinforce concepts and make this book appropriate for classroom use.

The table of contents for this book is given below.

1. Random Sampling 2. Point Estimation 3. Interval Estimation 4. Hypothesis Testing

Computational Graphics And Statistical Analysis: Mixed Type Random Variables, Confidence Regions, And Golden Quantile Rank Sets, Christopher Weld

Dissertations, Theses, and Masters Projects

This dissertation has three principle areas of research: mixed type random variables, confidence regions, and golden quantile rank sets. While each offers a specific focus, some common themes persist; broadly stated, there are three. First, computational graphics play a critical role. Second, software development facilitates implementation and accessibility. Third, statistical analysis---often attributable to the aforementioned automation---provides valuable insights and applications. Each of the principle research areas are briefly summarized next. Mixed type random variables are a hybrid of continuous and discrete random variables, having components of both continuous probability density and discrete probability mass. This dissertation illustrates the challenges inherent …

Introduction To "Probability", Lawrence Leemis

Arts & Sciences Book Chapters

This calculus-based introduction to probability covers all of the traditional topics, along with a secondary emphasis on Monte Carlo simulation. Examples that introduce applications from a wide range of fields help the reader apply probability theory to real-world problems. The text covers all of the topics associated with Exam P given by the Society of Actuaries. Over 100 figures highlight the intuitive and geometric aspects of probability. Over 800 exercises are used to reinforce concepts and make this text appropriate for classroom use.

Are Occupancy Models Feasible Alternatives To Collecting Breeding Data?, Morgan D. Niccoli

Dissertations, Theses, and Masters Projects

No abstract provided.

Status, Distribution And Reproductive Rates Of American Oystercatchers In Virginia, Alexandra Lee Wilke

Dissertations, Theses, and Masters Projects

No abstract provided.

Development Of Generalized Index-Removal Models, With Particular Attention To Catchability Issues, Thomas F. Ihde

Dissertations, Theses, and Masters Projects

The index-removal method estimates abundance, exploitation and catchability coefficient, given surveys conducted before and after a known removal. The method assumes a closed population between surveys. Index-removal has seldom been applied due to its strong assumption of constant survey catchabilities. This work generalizes the method to allow multiple years of data to be incorporated, and the assumptions of the original model to be relaxed. If catchability is constant across years, precision can be improved by analyzing multi-year data simultaneously. Two multiple-year models were developed: the first, 1qIR, assumes constant catchability within and among years; the second, 2qIR, allows catchability to …

Application Of Survival Analysis Methods To Pulsed Exposures: Exposure Duration, Latent Mortality, Recovery Time, And The Underlying Theory Of Survival Distribution Models, Yuan Zhao

Dissertations, Theses, and Masters Projects

Ecotoxicologists adopted median lethal concentration (LC50) methods from mammalian toxicology. This conventional LC50 approach has shortcomings. Fixing the exposure duration and selecting the 50% mortality level result in loss of ecologically relevant information generated at all other times. It also ignores latent mortality that can manifest after exposure ends. as a result, it cannot adequately predict pulsed exposure effects in which concentration, duration, and frequency of pulses change through time. The underlying theory of the dose-response models used to calculate LC50 values, stochastic versus individual effective dose (IED) theory, has not been tested rigorously either. In this study, the effects …

Status And Demographic Analysis Of The Dusky Shark, Carcharhinus Obscurus, In The Northwest Atlantic, Jason G. Romine

Dissertations, Theses, and Masters Projects

No abstract provided.

Simulation And Numerical Solution Of Stochastic Petri Nets With Discrete And Continuous Timing, Robert Linzey Jones Iii

Dissertations, Theses, and Masters Projects

We introduce a novel stochastic Petri net formalism where discrete and continuous phase-type firing delays can appear in the same model. By capturing deterministic and generally random behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity and efficiencies to use in practice. We formally specify the underlying stochastic process as a general state space Markov chain and show that it is regenerative, thus amenable to renewal theory techniques to obtain steady-state solutions. We present two steady-state analysis methods depending on the class of problem: one using exact numerical techniques, the other using simulation. Although regenerative …

A Numerical Simulation And Statistical Modeling Of High Intensity Radiated Fields Experiment Data, Laura Smith

Dissertations, Theses, and Masters Projects

No abstract provided.

Algorithms For Operations On Probability Distributions In A Computer Algebra System, Diane Lynn Evans

Dissertations, Theses, and Masters Projects

In mathematics and statistics, the desire to eliminate mathematical tedium and facilitate exploration has lead to computer algebra systems. These computer algebra systems allow students and researchers to perform more of their work at a conceptual level. The design of generic algorithms for tedious computations allows modelers to push current modeling boundaries outward more quickly.;Probability theory, with its many theorems and symbolic manipulations of random variables is a discipline in which automation of certain processes is highly practical, functional, and efficient. There are many existing statistical software packages, such as SPSS, SAS, and S-Plus, that have numeric tools for statistical …

A Probability Programming Language: Development And Applications, Andrew Gordon Glen

Dissertations, Theses, and Masters Projects

A probability programming language is developed and presented; applications illustrate its use. Algorithms and generalized theorems used in probability are encapsulated into a programming environment with the computer algebra system Maple to provide the applied community with automated probability capabilities. Algorithms of procedures are presented and explained, including detailed presentations on three of the most significant procedures. Applications that encompass a wide range of applied topics including goodness-of-fit testing, probabilistic modeling, central limit theorem augmentation, generation of mathematical resources, and estimation are presented.

Stock Enhancement Of Caribbean Spiny Lobster, Panulirus Argus Latrielle, Using Artificial Shelters: Patterns Of Survival And Dynamics Of Shelter Selection, David Bryan Eggleston

Dissertations, Theses, and Masters Projects

Field tethering experiments in seagrass beds of Bahia de la Ascension, Mexico examined the impact of different-sized artificial shelters upon survival of three juvenile size-classes of the Caribbean spiny lobster, Panulirus argus. The artificial shelters were concrete structures (casitas) that simulate lobster dens. In the tethering experiments, spiny lobster survival was generally higher in smaller than larger casitas, though the effect depended upon the relationship between lobster and shelter size. Thus, spiny lobster survival depends not only upon the availability of shelter, but also on the scaling between shelter size and lobster size. These results suggest that placement of appropriately-scaled …

Stock Identification Of Weakfish, Cynoscion Regalis, By Discriminant Function Analysis Of Morphometric Characters, Daniel R. Scoles

Dissertations, Theses, and Masters Projects

No abstract provided.

The Least Tern In Virginia: Breeding Biology And Population Distribution, John William Akers

Dissertations, Theses, and Masters Projects

No abstract provided.

A Numerical And Spatial Study Of The Meadow Vole, Microtus Pennsylvanicus, Margaret Whitney Higgins Bowker

Dissertations, Theses, and Masters Projects

No abstract provided.