Statistics and Probability Commons^™

Comparing Welch's Anova, A Kruskal-Wallis Test And Traditional Anova In Case Of Heterogeneity Of Variance, Hangcheng Liu

Theses and Dissertations

Analysis of variance (ANOVA) is a robust test against the normality assumption, but it may be inappropriate when the assumption of homogeneity of variance has been violated. Welch ANOVA and the Kruskal-Wallis test (a non-parametric method) can be applicable for this case. In this study we compare the three methods in empirical type I error rate and power, when heterogeneity of variance occurs and find out which method is the most suitable with which cases including balanced/unbalanced, small/large sample size, and/or with normal/non-normal distributions.

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Bayesian Inference Of The Weibull-Pareto Distribution, James Dow

College of Graduate Studies: Theses & Dissertations

The Weibull distribution has many applications in various topics. Some of these topics include survival analysis, reliability engineering, general insurance, electrical engineering, and industrial engineering. The Weibull distribution was further extended by the Weibull-Pareto distribution. A desirable property this distribution has is its shape can skew being able to better model left or right skewed data. Examples of skewed data include human longevity and actuarial data. In this work a hierarchical Bayesian model was developed using the Weibull-Pareto distribution.

Understanding Vulnerability In Alaska Fishing Communities: A Validation Methodology For Rapid Assessment Of Well-Being Indices, Conor M. Maguire

All Master's Theses

Social well-being indices measure how fishing communities are likely to be affected by social-ecological perturbations, and are a significant tool to identify the primary issues influencing communities’ sustained participation in fishing activities. In an attempt to further our understanding of how communities are affected by such perturbations, we have developed a rapid assessment methodology to test the external validity of a set of well-being indices that measure community vulnerability. This methodology informs how well such indices reflect the communities they represent by measuring elements of well-being through field observations, and comparing them to corresponding index components created from secondary data …

Meta-Analysis Of Gene Expression Studies, Umaporn Siangphoe

Theses and Dissertations

Combining effect sizes from individual studies using random-effects models are commonly applied in high-dimensional gene expression data. However, unknown study heterogeneity can arise from inconsistency of sample qualities and experimental conditions. High heterogeneity of effect sizes can reduce statistical power of the models. We proposed two new methods for random effects estimation and measurements for model variation and strength of the study heterogeneity. We then developed a statistical technique to test for significance of random effects and identify heterogeneous genes. We also proposed another meta-analytic approach that incorporates informative weights in the random effects meta-analysis models. We compared the proposed …

Application Of Loglinear Models To Claims Triangle Runoff Data, Netanya Lee Martin

Masters Theses

"In this thesis, we presented in detail different aspects of Verrall's chain ladder method and their advantages and disadvantages. Insurance companies must ensure there are enough reserves to cover future claims. To that end, it is useful to estimate mean expected losses. The chain ladder technique under a general linear model is the most widely used method for such estimation in property and casualty insurance. Verrall's chain ladder technique develops estimators for loss development ratios, mean expected ultimate claims, Bayesian premiums, and Bühlmann credibility premiums. The chain ladder technique can be used to estimate loss development in cases where data …

Space-Based Relative Multitarget Tracking, Keith Allen Legrand

Masters Theses

"Access to space has expanded dramatically over the past decade. The growing popularity of small satellites, specifically cubesats, and the following launch initiatives have resulted in exponentially growing launch numbers into low Earth orbit. This growing congestion in space has punctuated the need for local space monitoring and autonomous satellite inspection. This work describes the development of a framework for monitoring local space and tracking multiple objects concurrently in a satellite's neighborhood. The development of this multitarget tracking systems has produced collateral developments in numerical methods, relative orbital mechanics, and initial relative orbit determination.

This work belongs to a class …

Realistic Spiking Neuron Statistics In A Population Are Described By A Single Parametric Distribution, Lauren Crow 9370373

UROP Posters

The spiking of activity of neurons throughout the cortex is random and complicated. This complicated activity requires theoretical formulations in order to understand the underlying principles of neural processing. A key aspect of theoretical investigations is characterizing the probability distribution of spiking activity. This study aims to better understand the statistics of the time between spikes, or interspike interval, in both real data and a spiking model with many time scales. Exploration of the interspike intervals of neural network activity can provide a better understanding of neural responses to different stimuli. We consider different parametric distribution fitting techniques to characterize …

Bayesian Adaptive Penalized Splines In Nonparametric Regression And In Spectral Time Series Analysis, Luis Angel Mora

Open Access Theses & Dissertations

A Bayesian approach to nonparametric regression using Penalized splines (P-splines) is presented. The approach uses the linear mixed model formulation of P-spines. The usual model assumes a single value for the smoothing parameter controlling the amount of smoothing of the fitted function. The main focus of the Thesis is on spatially adaptive smoothing where the smoothing parameter is a function of the covariate so that different amounts of smoothing are applied in different regions of the covariate. An application to spectral time series analysis will be demonstrated. Markov chain Monte Carlo methods are used to make inference based on the …

Combining Semiparametric Regression And Kriging For Prediction Of Pm2.5 Pollutant Levels At Unmonitored Locations With Meterological And Traffic Data, Justin Jonathan Strate

Open Access Theses & Dissertations

Particulate matter (PM) is defined by the Texas Commission on Environmental Quality (TCEQ) as "a mixture of solid particles and liquid droplets found in the air". These particles vary widely in size. Those particles that are less than 2.5 micrometers in aerodynamic diameter are known as Particulate Matter 2.5 or PM2.5. These particles are inhaled, and their health effects are still largely being studied. Past studies have assessed PM2.5 exposure of a population, yet individual exposure is more diffcult to assess and may vary widely in a population. Recent studies have combined semiparametric models with kriging (Li et. al [2012]) …

Individual-Based Modeling: Mountain Pine Beetle Seasonal Biology In Response To Climate, Jacques Regniere, Barbara J. Bentz, James A. Powell, Remi St-Amant

Mathematics and Statistics Faculty Publications

Over the past decades, as significant advances were made in the availability and accessibility of computing power, individual-based models (IBM) have become increasingly appealing to ecologists (Grimm 1999). The individual-based modeling approachprovides a convenient framework to incorporate detailed knowledge of individuals and of their interactions within populations (Lomnicki 1999). Variability among individuals is essential to the success of populations that are exposed to changing environments, and because natural selection acts on this variability, it is an essential component of population performance. © Springer International Publishing Switzerland 2015.

Controlling For Confounding When Association Is Quantified By Area Under The Roc Curve, Hadiza I. Galadima

Theses and Dissertations

In the medical literature, there has been an increased interest in evaluating association between exposure and outcomes using nonrandomized observational studies. However, because assignments to exposure are not done randomly in observational studies, comparisons of outcomes between exposed and non-exposed subjects must account for the effect of confounders. Propensity score methods have been widely used to control for confounding, when estimating exposure effect. Previous studies have shown that conditioning on the propensity score results in biased estimation of odds ratio and hazard ratio. However, there is a lack of research into the performance of propensity score methods for estimating the …

Fact Sheet, Yale University Office Of Institutional Research

Fact Sheets

No abstract provided.

Statistical Modeling Of Microrna Expression With Human Cancers, Ke-Sheng Wang, Yue Pan, Chun Xu

Health & Biomedical Sciences Faculty Publications

MicroRNAs (miRNAs) are small non-coding RNAs (containing about 22 nucleotides) that regulate gene expression. MiRNAs are involved in many different biological processes such as cell proliferation, differentiation, apoptosis, fat metabolism, and human cancer genes; while miRNAs may function as candidates for diagnostic and prognostic biomarkers and predictors of drug response. This paper emphasizes the statistical methods in the analysis of the associations of miRNA gene expression with human cancers and related clinical phenotypes: 1) simple statistical methods include chi-square test, correlation analysis, t-test and one-way ANOVA; 2) regression models include linear and logistic regression; 3) survival analysis approaches such as …

Inequalities And Approximations Of Weighted Distributions By Lindley Reliability Measures, And The Lindley-Cox Model With Applications, Broderick O. Oluyede, Macaulay Okwuokenye, Karl E. Peace

Biostatistics: Faculty Publications

In this note, stochastic comparisons and results for weighted and Lindley models are presented. Approximation of weighted distributions via Lindley distribution in the class of increasing failure rate (IFR) and decreasing failure rate (DFR) weighted distributions with monotone weight functions are obtained including approximations via the length-biased Lindley distribution. Some useful bounds and moment-type inequality for weighted life distributions and applications are presented. Incorporation of covariates into Lindley model is considered and an application to illustrate the usefulness and applicability of the proposed Lindley-Cox model is given.

How Long Does That 10-Year Smoke Alarm Really Last? A Survival Analysis Of Smoke Alarms Installed Through The Saife Program In Rural Georgia, Haresh Rochani, Valamar Malika Reagon, Steve Davidson

Biostatistics: Faculty Publications

Background: When functioning properly, a smoke alarm alerts individuals in the residence that smoke is near the alarm. Smoke alarms serve as a primary prevention mechanism to abate morbidity and mortality related to residential fires.

Methods: Using survival analysis, we examined the length of operability of 10-year lithium battery powered smoke alarms installed through the Georgia Public Health/CDC SAIFE program in Moultrie, Georgia. Attempts were made to reach all homes in the city limits. The premise of the study is that geographic clusters (in the case of Moultrie city quadrants) are associated with decreases in the length of time that …

Graph-Based Regularization In Machine Learning: Discovering Driver Modules In Biological Networks, Xi Gao

Theses and Dissertations

Curiosity of human nature drives us to explore the origins of what makes each of us different. From ancient legends and mythology, Mendel's law, Punnett square to modern genetic research, we carry on this old but eternal question. Thanks to technological revolution, today's scientists try to answer this question using easily measurable gene expression and other profiling data. However, the exploration can easily get lost in the data of growing volume, dimension, noise and complexity. This dissertation is aimed at developing new machine learning methods that take data from different classes as input, augment them with knowledge of feature relationships, …

Small Sample Saddlepoint Confidence Intervals In Epidemiology, Pasan Manuranga Edirisinghe

Doctoral Dissertations

"In section 1, we develop a novel method of confidence interval construction for directly standardized rates. These intervals involve saddlepoint approximations to the intractable distribution of a weighted sum of Poisson random variables and the determination of hypothetical Poisson mean values for each of the age groups. Simulation studies show that, in terms of coverage probability and length, the saddlepoint confidence interval (SP) outperforms four competing confidence intervals obtained from the moment matching (M8), gamma-based (G1,G4) and ABC bootstrap (ABC) methods.

In section 2, we first consider Brillinger's classical model for a vital rate estimate with a random denominator. We …

A Domain Decomposition Method For The Steady-State Navier-Stokes-Darcy Model With Beavers-Joseph Interface Condition, Xiaoming He, Jian Li, Yanping Lin, Ju Ming

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes and analyzes a Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier-Stokes-Darcy model with three interface conditions. In addition to the two regular interface conditions for the mass conservation and the force balance, the Beavers-Joseph condition is used as the interface condition in the tangential direction. The major mathematical difficulty in adopting the Beavers-Joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system [Y. Cao et al., Comm. Math. Sci., 8 (2010), pp. 1-25; Y. Cao et al., SIAM J. Numer. Anal., 47 (2010), pp. 4239-4256]. In …

The Role Of Citizens In Detecting And Responding To A Rapid Marine Invasion, Steven B. Scyphers, Sean P. Powers, J. Lad Akins, J. Marcus Drymon, Charles W. Martin, Zeb H. Schobernd, Pamela J. Schofield, Robert L. Shipp, Theodore S. Switzer

University Faculty and Staff Publications

Documenting and responding to species invasions requires innovative strategies that account for ecological and societal complexities. We used the recent expansion of Indo-Pacific lionfish (Pterois volitans/miles) throughout northern Gulf of Mexico coastal waters to evaluate the role of stakeholders in documenting and responding to a rapid marine invasion. We coupled an online survey of spearfishers and citizen science monitoring programs with traditional fishery-independent data sources and found that citizen observations documented lionfish 1–2 years earlier and more frequently than traditional reef fish monitoring programs. Citizen observations first documented lionfish in 2010 followed by rapid expansion and proliferation in …