Statistics and Probability Commons^™

The Doubly Inflated Poisson And Related Regression Models, Manasi Sheth-Chandra

Mathematics & Statistics Theses & Dissertations

Most real life count data consists of some values that are more frequent than allowed by the common parametric families of distributions. For data consisting of only excess zeros, in a seminal paper Lambert (1992) introduced Zero-Inflated Poisson (ZIP) model, which is a mixture model that accounts for the inflated zeros. In this thesis, two Doubly Inflated Poisson (DIP) probability models, DIP (p, λ) and DIP ( p1, p2, λ), are discussed for situations where there is another inflated value k > 0 besides the inflated zeros. The distributional properties such as identifiability, moments, and conditional probabilities …

On The Use Of Log-Transformation Vs. Nonlinear Regression For Analyzing Biological Power-Laws, Xiao Xiao

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Power-law relationships are among the most well-studied functional relationships in biology . Recently the common practice of fitting power-laws using linear regression on log-transformed data (LR) has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations we demonstrate that the error distribution determines which method performs better, with LR better characterizing data with multiplicative lognormal error and NLR better characterizing data with additive normal error. Analysis of 471 biological power-laws shows that both …

Development And Implementation Of A Bayesian Model For Sediment Transport In Fluvial Systems, Mark Schmelter

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Recent studies in the field of fluvial sediment transport underscore the difficulty in reliably estimating transport model parameters, collecting accurate observations, and making predictions due to measurement error and conceptual model uncertainty. There is a pressing need to develop models that can account for measurement error, conceptual model uncertainty, and natural variability while providing probability-based predictions as well as a means for conceptual model discrimination. The model presented in this research employs an excess shear sediment transport equation for a uni-size sediment bed developed in a Bayesian statistical framework. This statistical model provides a means to rigorously estimate distributions of …

Assessing Measurement Invariance In The Presence Of Testlets, Luis Andres Alvarado

Open Access Theses & Dissertations

Dealing with measurement invariance has been an issue of concern in confirmatory factor analysis for many years. It is important to establish measurement invariance across groups so that instruments may be validly used in multiple groups for comparison of the mean or summative scores. Throughout the years, many studies have considered testing for measurement invariance in factor models. However, there have been no studies that assess measurement invariance when so-called testlets should be modeled in the factor analytic model. Testlets add nuisance covariation to the model which can interfere when trying to detect measurement invariance. In the past, models have …

Estimating The Effect Of Dust And Low Wind Events On Hospitalizations For Asthma While Adjusting For Hourly Levels Of Air Pollutants, Priyangi Kanchana Bulathsinhala

Open Access Theses & Dissertations

El Paso, Texas is known as one of the dust hotspots in North America. We explore the effect of dust and low wind events on asthma admissions in El Paso, Texas between 2000 and 2005. Conditional logistic regression with a case-crossover design was used to estimate the probability of hospitalization after dust and low wind events while controlling for pollutants with hourly monitor measurements, and weather. The historical functional linear model is used to incorporate the hourly pollutant measures into the regression model with a continuous lag, as an alternative to a distributed lag model based on daily averages. The …

Estimating Statistical Characteristics Under Interval Uncertainty And Constraints: Mean, Variance, Covariance, And Correlation, Ali Jalal-Kamali

Open Access Theses & Dissertations

In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, . . . , xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation.

The values xi come from measurements, and measurement is never absolutely accurate.

Often, …

Autonomous Entropy-Based Intelligent Experimental Design, Nabin Kumar Malakar

Legacy Theses & Dissertations (2009 - 2024)

The aim of this thesis is to explore the application of probability and information theory in experimental design, and to do so in a way that combines what we know about inference and inquiry in a comprehensive and consistent manner.

Drag Reduction Of A Modern Straight Truck, Drew Landman, Matthew Cragun, Mike Mccormick, Richard Wood

Mechanical & Aerospace Engineering Faculty Publications

A wind tunnel test program was conducted at the Langley Full Scale Tunnel (LFST) to evaluate the performance of five passive drag reduction configurations on a modern straight truck at full scale. Configurations were tested in a build-up fashion with results representing a cumulative effect. Tested configurations include a front valance, a front box fairing, a boat-tail, an ideal side-skirt, and a practical side-skirt. Configurations were evaluated over a nominal 9 degree yaw sweep to establish wind averaged drag coefficients using SAE J1252. Genuine replicate yaw sweeps were used in an uncertainty analysis. Results show up to 28% improvement in …

Computational Methods Of Hidden Markov Models With Respect To Cpg Island Prediction In Dna Sequences, Roberto Angel Ortega

Open Access Theses & Dissertations

Hidden Markov models (HMM's) are a specific case of Markov models where, contrary to Markov chains, the observer is unaware of what state the model was in when the symbol is observed. Like Markov chains, HMM's assume that the future state of a sequence is dependent only on the current state of the sequence. The parameters associated with HMM's are transition and emission probabilities, where transition probabilities are associated with the probability of transitioning from one state to another, and emission probabilities are the probabilities associated with observing a symbol given it came from a specific state.

The structure of …

Essays On Hedge Fund Replication: Methodological Assessment And Development Of The Factor Approach, Nonlinear Modeling And Policy Perspectives, Guillaume Weisang

2011

This dissertation is concerned with hedge fund replication, a subject of a practical and theoretical importance, both from an investment and a risk management point of view. One of our goals is to extend known methodologies in order to enhance our understanding of an industry that is known for its secrecy and its lack of transparency. A second goal is to contribute to the quantitative finance literature with improved techniques for hedge fund replication. Hedge fund replication (HFR) is approached from the methodological as well as from practical and regulatory perspectives. The first two chapters provide the motivation and the …

Parametric Estimation In Competing Risks And Multi-State Models, Yushun Lin

Theses and Dissertations--Statistics

The typical research of Alzheimer's disease includes a series of cognitive states. Multi-state models are often used to describe the history of disease evolvement. Competing risks models are a sub-category of multi-state models with one starting state and several absorbing states.

Analyses for competing risks data in medical papers frequently assume independent risks and evaluate covariate effects on these events by modeling distinct proportional hazards regression models for each event. Jeong and Fine (2007) proposed a parametric proportional sub-distribution hazard (SH) model for cumulative incidence functions (CIF) without assumptions about the dependence among the risks. We modified their model to …

Stochastic Dynamics Of Gene Transcription, Yan Xie

Theses and Dissertations--Statistics

Gene transcription in individual living cells is inevitably a stochastic and dynamic process. Little is known about how cells and organisms learn to balance the fidelity of transcriptional control and the stochasticity of transcription dynamics. In an effort to elucidate the contribution of environmental signals to this intricate balance, a Three State Model was recently proposed, and the transcription system was assumed to transit among three different functional states randomly.

In this work, we employ this model to demonstrate how the stochastic dynamics of gene transcription can be characterized by the three transition parameters. We compute the probability distribution of …

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman

Mathematics Faculty Publications

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Mathematics Faculty Publications

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler

Mathematics Faculty Publications

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.

Ohio's Use Of Geographic Information Systems To Demonstrate Public Participation In The Redistricting Process, Mark Salling

All Maxine Goodman Levin School of Urban Affairs Publications

No abstract provided.

Public Participation Geographic Information Systems For Redistricting A Case Study In Ohio, Mark Salling

All Maxine Goodman Levin School of Urban Affairs Publications

Public Participation Geographic Information Systems for Redistricting A Case Study in Ohio, Journal of the Urban and Regional Information Systems Association, Vol. 23, Number 1, forthcoming.

Drift And The Risk-Free Rate, Anda Gadidov, M. C. Spruill

Faculty Articles

It is proven, under a set of assumptions differing from the usual ones in the unboundedness of the time interval, that, in an economy in equilibrium consisting of a risk-free cash account and an equity whose price process is a geometric Brownian motion on [0,∞), the drift rate must be close to the risk-free rate; if the drift rate μ and the risk-free rate r are constants, then r = μ and the price process is the same under both empirical and risk neutral measures. Contributing in some degree perhaps to interest in this mathematical curiosity is the fact, based …

Adjusted Empirical Likelihood Models With Estimating Equations For Accelerated Life Tests, Ni Wang, Jye-Chyi Lu, Di Chen, Paul H. Kvam

Department of Math & Statistics Faculty Publications

This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology.

Multi-Cause Degradation Path Model: A Case Study On Rubidium Lamp Degradation, Sun Quan, Paul H. Kvam

Department of Math & Statistics Faculty Publications

At the core of satellite rubidium standard clocks is the rubidium lamp, which is a critical piece of equipment in a satellite navigation system. There are many challenges in understanding and improving the reliability of the rubidium lamp, including the extensive lifetime requirement and the dearth of samples available for destructive life tests. Experimenters rely on degradation experiments to assess the lifetime distribution of highly reliable products that seem unlikely to fail under the normal stress conditions, because degradation data can provide extra information about product reliability. Based on recent research on the rubidium lamp, this article presents a multi‐cause …

Adjusted Hazard Rate Estimator Based On A Known Censoring Probability, Ülkü Gürler, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In most reliability studies involving censoring, one assumes that censoring probabilities are unknown. We derive a nonparametric estimator for the survival function when information regarding censoring frequency is available. The estimator is constructed by adjusting the Nelson–Aalen estimator to incorporate censoring information. Our results indicate significant improvements can be achieved if available information regarding censoring is used. We compare this model to the Koziol–Green model, which is also based on a form of proportional hazards for the lifetime and censoring distributions. Two examples of survival data help to illustrate the differences in the estimation techniques.

Evaluating Methods For The Analysis Of Rare Variants In Sequence Data, Alexander Luedtke, Scott Powers, Ashley Petersen, Alexandra Sitarik, Airat Bekmetjev, Nathan L. Tintle

Faculty Work Comprehensive List

A number of rare variant statistical methods have been proposed for analysis of the impending wave of next-generation sequencing data. To date, there are few direct comparisons of these methods on real sequence data. Furthermore, there is a strong need for practical advice on the proper analytic strategies for rare variant analysis. We compare four recently proposed rare variant methods (combined multivariate and collapsing, weighted sum, proportion regression, and cumulative minor allele test) on simulated phenotype and next-generation sequencing data as part of Genetic Analysis Workshop 17. Overall, we find that all analyzed methods have serious practical limitations on identifying …

Evaluating Methods For Combining Rare Variant Data In Pathway-Based Tests Of Genetic Association, Ashley Petersen, Alexandra Sitarik, Alexander Luedtke, Scott Powers, Airat Bekmetjev, Nathan L. Tintle

Faculty Work Comprehensive List

Analyzing sets of genes in genome-wide association studies is a relatively new approach that aims to capitalize on biological knowledge about the interactions of genes in biological pathways. This approach, called pathway analysis or gene set analysis, has not yet been applied to the analysis of rare variants. Applying pathway analysis to rare variants offers two competing approaches. In the first approach rare variant statistics are used to generate p-values for each gene (e.g., combined multivariate collapsing [CMC] or weighted-sum [WS]) and the gene-level p-values are combined using standard pathway analysis methods (e.g., gene set enrichment analysis or …

Identifying Rare Variants From Exome Scans: The Gaw17 Experience, Saurabh Ghosh, Heike Bickeboller, Julia Bailey, Joan E. Bailey-Wilson, Rita Cantor, Robert Culverhouse, Warwick Daw, Anita L. Destefano, Corinne D. Engelman, Anthony Hinrichs, Jeanine Houwing-Duistermaat, Inke R. Konig, Jack Kent, Nan Laird, Nathan Pankratz, Andrew Paterson, Elizabeth Pugh, Brian Suarez, Yan Sun, Alun Thomas, Nathan L. Tintle, Xiaofeng Zhu, Andreas Ziegler, Jean W. Maccluer, Laura Almasy

Faculty Work Comprehensive List

Genetic Analysis Workshop 17 (GAW17) provided a platform for evaluating existing statistical genetic methods and for developing novel methods to analyze rare variants that modulate complex traits. In this article, we present an overview of the 1000 Genomes Project exome data and simulated phenotype data that were distributed to GAW17 participants for analyses, the different issues addressed by the participants, and the process of preparation of manuscripts resulting from the discussions during the workshop

Longitudinal Investigation Of The Curricular Effect: An Analysis Of Student Learning Outcomes From The Liecal Project In The United States, Jinfa Cai, Ning Wang, John Moyer, Chuang Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including …

Bayesian Item Response Theory: Statistical Inference And Power Analysis, Jason W. Bodnar

Dissertations

The regulatory pharmaceutical approval process is flawed in that industry clinical trials (ICTs) are always powered for efficacy and rarely powered for safety. The key safety parameter is the adverse event (AE). This practice may result in efficacious products with confounded safety. An ICT’s ability to be powered for detecting AE trends may improve patient safety. Therefore, this dissertation’s purpose was to determine if power analysis resulted in feasible sample sizes for substantiating AE hypotheses. AEs were modeled with three Bayesian 2PL IRT models. The unidimensional latent trait, transfusion-related AE, was modeled as a patient predisposition for experiencing an AE. …

Statistician Recommends A Dose Of Skepticism, Aldemaro Romero Jr.

Publications and Research

No abstract provided.

Neath Studies, Teaches The Uncertainties Of Life, Aldemaro Romero Jr.

Publications and Research

No abstract provided.

Some Contributions To The Censored Empirical Likelihood With Hazard-Type Constraints, Yanling Hu

University of Kentucky Doctoral Dissertations

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. Owen’s 2001 book contains many important results for EL with uncensored data. However, fewer results are available for EL with right-censored data. In this dissertation, we first investigate a right-censored-data extension of Qin and Lawless (1994). They studied EL with uncensored data when the number of estimating equations is larger than the number of parameters (over-determined case). We obtain results similar to theirs for the maximum EL estimator and the EL ratio test, for the over-determined case, with right-censored data. We employ hazard-type constraints which are better able …

Studies In Sampling Techniques And Time Series Analysis, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

This book has been designed for students and researchers who are working in the field of time series analysis and estimation in finite population. There are papers by Rajesh Singh, Florentin Smarandache, Shweta Maurya, Ashish K. Singh, Manoj Kr. Chaudhary, V. K. Singh, Mukesh Kumar and Sachin Malik. First chapter deals with the problem of time series analysis and the rest of four chapters deal with the problems of estimation in finite population. The book is divided in five chapters as follows: Chapter 1. Water pollution is a major global problem. In this chapter, time series analysis is carried out …