Applied Statistics Commons^™

Zero-Inflated Models To Identify Transcription Factor Binding Sites In Chip-Seq Experiments, Sameera Dhananjaya Viswakula

Mathematics & Statistics Theses & Dissertations

It is essential to determine the protein-DNA binding sites to understand many biological processes. A transcription factor is a particular type of protein that binds to DNA and controls gene regulation in living organisms. Chromatin immunoprecipitation followed by highthroughput sequencing (ChIP-seq) is considered the gold standard in locating these binding sites and programs use to identify DNA-transcription factor binding sites are known as peak-callers. ChIP-seq data are known to exhibit considerable background noise and other biases. In this study, we propose a negative binomial model (NB), a zero-inflated Poisson model (ZIP) and a zero-inflated negative binomial model (ZINB) for peak-calling. …

Analysis Of Continuous Longitudinal Data With Arma(1, 1) And Antedependence Correlation Structures, Sirisha Mushti

Mathematics & Statistics Theses & Dissertations

Longitudinal or repeated measure data are common in biomedical and clinical trials. These data are often collected on individuals at scheduled times resulting in dependent responses. Inference methods for studying the behavior of responses over time as well as methods to study the association with certain risk factors or covariates taking into account the dependencies are of great importance. In this research we focus our study on the analysis of continuous longitudinal data. To model the dependencies of the responses over time, we consider appropriate correlation structures generated by the stationary and non-stationary time-series models. We develop new estimation procedures …

Modeling Martian Planetary Entry Descent And Landing Using Monte Carlo Driven Response Surface Methodology, Narcrisha S. Norman

Mechanical & Aerospace Engineering Theses & Dissertations

Response surface methodology (RSM) is a statistical method that explores the relationships between several descriptive variables and one or more response variables. For over sixty years, among other areas, it has been utilized in quality engineering, process engineering, aircraft engineering, economics, chemical engineering, automotive engineering and design/technique optimization. In this dissertation, RSM is utilized to produce regression models that represent the planetary entry, descent and landing (EDL) process. A complete understanding of EDL process is an essential component of any planetary exploration. Research in this area is ongoing and confidence in the ability to explore known celestial bodies is growing. …

Meta-Heuristics Analysis For Technologically Complex Programs: Understanding The Impact Of Total Constraints For Schedule, Quality And Cost, Henry Darrel Webb

EMSE Doctoral Projects

Program management data associated with a technically complex radio frequency electronics base communication system has been collected and analyzed to identify heuristics which may be utilized in addition to existing processes and procedures to provide indicators that a program is trending to failure. Analysis of the collected data includes detailed schedule analysis, detailed earned value management analysis and defect analysis within the framework of a Firm Fixed Price (FFP) incentive fee contract.

This project develops heuristics and provides recommendations for analysis of complex project management efforts such as those discussed herein. The analysis of the effects of the constraints on …

Response Surface Optimization Of Electron Beam Freeform Fabrication Depositions Using Design Of Experiments, Patricia A. Quigley

Engineering Management & Systems Engineering Theses & Dissertations

The Electron Beam Freeform Fabrication (EBF³ ) System is a material depositing, layer additive technique that produces three dimensional (3D) parts out of a wide range of metals in high vacuum, using an electron beam and wire feedstock. Screening deposition trials on a titanium alloy, Ti-6Al-4V, at the National Aeronautics Space Administration (NASA) revealed selective vaporization of the aluminum content of linear prototypes when subjected to chemical analysis. In this study, the aluminum content, bead height and bead width output responses were analyzed from a systematic study of the effects that the interactions of the EBF³ processing parameters …

A Statistical Model To Determine Multiple Binding Sites Of A Transcription Factor On Dna Using Chip-Seq Data, Rasika Jayatillake

Mathematics & Statistics Theses & Dissertations

Protein-DNA interaction is vital to many biological processes in cells such as cell division, embryo development and regulating gene expression. Chromatin Immunoprecipitation followed by massively parallel sequencing (ChIP-seq) is a new technology that can reveal protein binding sites in genome with superior accuracy. Although many methods have been proposed to find binding sites for ChIP-seq data, they can find only one binding site within a short region of the genome. In this study we introduce a statistical model to identify multiple binding sites of a transcription factor within a short region of the genome using the ChIP-seq data. Mapped sequence …

Analysis Of Discrete Choice Probit Models With Structured Correlation Matrices, Bhaskara Ravi

Mathematics & Statistics Theses & Dissertations

Discrete choice models are very popular in Economics and the conditional logit model is the most widely used model to analyze consumer choice behavior, which was introduced in a seminal paper by McFadden (1974). This model is based on the assumption that the unobserved factors, which determine the consumer choices, are independent and follow a Gumbel distribution, widely known as the Independence of irrelevant Alternatives (IIA) assumption. Alternate models that relax IIA assumption are the Generalized Extreme Value (GEV) models, which allow dependency between unobserved factors. However, GEV models do not incorporate all dependency patterns, other choice behaviors such as …

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 …

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

Mathematics & Statistics Theses & Dissertations

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the …

Canonical Correlation Analysis For Longitudinal Data, Raymond Mccollum

Mathematics & Statistics Theses & Dissertations

Data (multivariate data) on two sets of vectors commonly occur in applications. Statistical analysis of these data is usually done using a canonical correlation analysis (CCA). Occurrence of these data at multiple occasions or conditions leads to longitudinal multivariate data for a CCA. We address the problem of canonical correlation analysis on longitudinal data when the data have a Kronecker product covariance structure. Using structured correlation matrices we model the dependency of repeatedly observed data. Recent work of Srivastava, Nahtman, and von Rosen (2008) developed an iterative algorithm to determine the maximum likelihood estimate of the Kronecker product covariance structure …

Canonical Correlation And Correspondence Analysis Of Longitudinal Data, Jayesh Srivastava

Mathematics & Statistics Theses & Dissertations

Assessing the relationship between two sets of multivariate vectors is an important problem in statistics. Canonical correlation coefficients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. When the variables are qualitative (categorical), a technique called correspondence analysis (CA) is used. Canonical correspondence analysis (CCPA) is used to deal with the case when one set of variables is categorical and the other set is quantitative. By exploiting the interrelationships between these three techniques we first provide a theoretical basis for …

Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo

Mathematics & Statistics Theses & Dissertations

Familial data occur when observations are taken on multiple members of the same family. Due to relationships between these members, both genetic and by cohabitation, their response variables will likely exhibit some form of dependence. Most of the existing literature models this dependence with an equicorrelated structure. This structure is appropriate when the dependencies between family members are similar, such as in genetic studies, but not in cases where we expect the dependencies to differ, such as behavioral comparisons across different age groups. In this dissertation we first discuss an alternative structure based upon first-order autoregressive correlation. Specifically we create …

Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng

Mathematics & Statistics Theses & Dissertations

Analysis of dependent continuous and discrete data has become an active area of research. For normal data, correlations fully quantify the dependence. And historically, maximum likelihood method has been very successful to estimate the correlations and unbiased estimating equation approach has become a popular alternative when there may be a departure from normality. In this thesis we show that the optimal unbiased estimating equation coincides with the likelihood equations for normal data. We then introduce a general class of weighted unbiased estimating equations to estimate parameters in a structured correlation matrix. We derive expressions for asymptotic covariance of the estimates, …

Mark-Recapture Creel Survey And Survival Models, Shampa Saha

Mathematics & Statistics Theses & Dissertations

In this dissertation, we consider a model based approach to the estimation of exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We also consider the analysis of a proportional hazards survival model for randomly censored observations, known as the Koziol-Green model. The model assumes that the lifetime survivor function is a power of the censored time survivor function.

In Chapter 2, we introduce the model based approach to the estimation of the exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We assume that in the beginning of a …

Analysis Of Repeated Measures Data Under Circular Covariance, Andrew Montgomery Hartley

Mathematics & Statistics Theses & Dissertations

Circular covariance is important in modelling phenomena in epidemiological, communications and numerous physical contexts. We introduce and develop a variety of methods which make it a more versatile tool. First, we present two classes of estimators for use in the presence of missing observations. Using simulations, we show that the mean squared errors of the estimators of one of these classes are smaller than those of the Maximum Likelihood (ML) estimators under certain conditions. Next, we propose and discuss a parsimonious, autoregressive type of circular covariance structure which involves only two parameters. We specify ML and other types of estimators …

The Use Of A Factory Simulation To Evaluate A Flexible Control Structure For Integrated Manufacturing, Ling Ling Pan

Engineering Management & Systems Engineering Theses & Dissertations

Once a control structure for an integrated manufacturing system is decided upon, manufacturing activities are limited by that structure. A flexible control structure is presented as an approach for accommodating a variety of manufacturing activities, without being limited to a single control structure. A flexible control structure is one that allows multiple types of control structure in the manufacturing process. For example, both hierarchical and non-hierarchical structures may be used in a flexible structure. The properties of a flexible control structure are discussed from the point of view of graph theory.

Control structures for automated manufacturing are difficult to evaluate …

Multidimensional Approach To Implementation Of Continuous Process Improvement Utilizing Small Run Analysis In A Shipyard Environment, Paul Ray Hollandsworth

Engineering Management & Systems Engineering Theses & Dissertations

Nationally, both public and private shipyards are experiencing a high rework rate (over 40%) in the fabrication of plug connectors used for electronic systems onboard Navy vessels. The shipyard's survival depends on acquiring the elements necessary to maintain a major industry in a position of continuous improvement that produces a better product than their competitors, at less cost, in a safe manner, and on schedule.

This research addresses the complex problem of how to introduce quality control methodologies within a job shop environment that assists in identifying variables that influence the rework rate of plug fabrication process over a four …

Reliability Trend Analyses With Statistical Confidence Limits Using The Luke Reliability Trend Chart, Stephen R. Luke

Engineering Management & Systems Engineering Theses & Dissertations

In electronic systems, it is interesting to understand exactly how the reliability is changing with time. Dynamic performance changes when a system passes from infant mortality stage into useful life phase and when the system passes from useful life phase into wearout phase. Dynamic performance also changes when the system is redesigned or when the system is acted on by a number of other outside forces such as a change in maintenance policy, escalation of alignment problems, or a change in training program. It is important to know when a system is changing dynamically in order to assess design, policy …

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

The Truncated Cauchy Distribution: Estimation Of Parameters And Application To Stock Returns, Paul G. Staneski

Mathematics & Statistics Theses & Dissertations

The problem addressed in this dissertation is the existence and estimation of the parameters of a truncated Cauchy distribution. It is known that when a number of distributions with infinite support are truncated to a finite interval that the maximum likelihood estimator of the scale parameter fails to exist with positive probability. In particular, necessary and sufficient conditions which give rise to instances of non-existence have been found for the exponential (Deemer and Votaw (1955)), gamma (Broeder (1955), Hegde and Dahiya (1989)), Weibull (Mittal and Dahiya (1989)) and normal distribution (Barndorff-Nielsen (1978), Mittal and Dahiya (1987), Hegde and Dahiya (1989)). …

Software Reliability Models, Syed Afzal Hossain

Mathematics & Statistics Theses & Dissertations

The problem considered here is the building of Non-homogeneous Poisson Process (NHPP) model. Currently existing popular NHPP process models like Goel-Okumoto (G-O) and Yamada et al models suffer from the drawback that the probability density function of the inter-failure times is an improper density function. This is because the event no failure in (0, oo] is allowed in these models. In real life situations we cannot draw sample(s) from such a population and also none of the moments of inter-failure times exist. Therefore, these models are unsuitable for modelling real software error data. On the other hand if the density …

Optimal Row-Column Designs For Correlated Errors And Nested Row-Column Designs For Uncorrelated Errors, Nizam Uddin

Mathematics & Statistics Theses & Dissertations

In this dissertation the design problems are considered in the row-column setting for second order autonormal errors when the treatment effects are estimated by generalized least squares, and in the nested row-column setting for uncorrelated errors when the treatment effects are estimated by ordinary least squares. In the former case, universal optimality conditions are derived separately for designs in the plane and on the torus using more general linear models than those considered elsewhere in the literature. Examples of universally optimum planar designs are given, and a method is developed for the construction of optimum and near optimum designs, that …

Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis

Mathematics & Statistics Theses & Dissertations

Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {S_n, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø_1n and Ø_2n be the moment genereating functions of {Tn, n > 1} and { S_n,n > 1} respectively. Let {a_n} be a sequence of real numbers such that a_n —»• oo.

Statistical Calibration Theory, James John Mckeon

Mathematics & Statistics Theses & Dissertations

A calibration method substitutes for measurements, X(,i), that are accurate but impractical or costly, a set of measurements, Y(,i), that are less accurate but simpler or less costly. There are two general types of calibration methods. The classical approach in which once the calibration sample is drawn, the estimates of the X values for a given unit is found without any consideration of the distribution of X values for the other units to be measured. This corresponds best to the literal meaning of the word "calibration". Maximum likelihood estimation is the statistical formulation of the classical approach.

The second approach …