Statistics and Probability Commons^™

Acceptance-Rejection Sampling With Hierarchical Models, Christian A. Ayala

CMC Senior Theses

Hierarchical models provide a flexible way of modeling complex behavior. However, the complicated interdependencies among the parameters in the hierarchy make training such models difficult. MCMC methods have been widely used for this purpose, but can often only approximate the necessary distributions. Acceptance-rejection sampling allows for perfect simulation from these often unnormalized distributions by drawing from another distribution over the same support. The efficacy of acceptance-rejection sampling is explored through application to a small dataset which has been widely used for evaluating different methods for inference on hierarchical models. A particular algorithm is developed to draw variates from the posterior …

Derivation And Validation Of The Friction, Gravitational, And Air Forces Encountered During Installation Of Fiber Optic Cable, Faheed Olayemi Owokoniran

All Graduate Theses, Dissertations, and Other Capstone Projects

This paper presents an introduction to fiber optic cable and the fiber optic communication system. An important phase in the supply of this new technology is to transport the fiber optic cable to the vicinity of service. Cable pulling and cable blowing - laminar flow; piston type - are the two main methods of installing fiber optic cable. Both methods of installation have limiting factors that need to be evaluated in order to perform a successful installation. The limiting factors for laminar type cable blowing are further discussed in this paper. A method was proposed to determine the forces - …

Combinatorially Interpreting Generalized Stirling Numbers, John Engbers, David Galvin, Justin Hilyard

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Exponentially Increasing Incidences Of Cutaneous Malignant Melanoma In Europe Correlate With Low Personal Annual Uv Doses And Suggests 2 Major Risk Factors, Stephen Merrill, Samira Ashrafi, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

For several decades the incidence of cutaneous malignant melanoma (CMM) steadily increased in fair-skinned, indoor-working people around the world. Scientists think poor tanning ability resulting in sunburns initiate CMM, but they do not understand why the incidence continues to increase despite the increased use of sunscreens and formulations offering more protection. This paradox, along with lower incidences of CMM in outdoor workers, although they have significantly higher annual UV doses than indoor workers have, perplexes scientists. We found a temporal exponential increase in the CMM incidence indicating second-order reaction kinetics revealing the existence of 2 major risk factors. From epidemiology …

Characterizations Of Transmuted Complementary Weibull Geometric Distribution, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present certain characterizations of a recently introduced distribution (Afify et al., 2014), called Transmuted Complementary Weibull Geometric distribution based on: hazard function ; a simple relation between two truncated moments. We like to mention that the characterization which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. It does not require a closed form for the cumulative distribution function and serves as a bridge between a first order differential equation and probability.

Characterizations Of Nwp, Etgr And Twl Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Utilizing a simple relationship between two truncated moments as well as certain functions of the 1st and of the nth order statistics, we characterize three extended classes of distributions proposed in (2015).

Characterizations Of Distributions Via Conditional Expectation Of Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics.

Signal Processing Spreads A Voxel’S Temporal Frequency Task-Activated Peak And Induces Spatial Correlations In Dual-Task Complex-Valued Fmri, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

The Transmuted Exponentiated Generalized-G Family Of Distributions, Haitham M. Yousof, Ahmed Z. Afify, Morad Alizadeh, Nadeem Shafique Butt, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new class of continuous distributions called the transmuted exponentiated generalized-G family which extends the exponentiated generalized-G class introduced by Cordeiro et al. (2013). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of an applications to real dataset.

Characteristics Of Feedback That Influence Student Confidence And Performance During Mathematical Modeling, Hyunyi Jung, Heidi A. Diefes-Dux, Aladar K. Horvath, Kelsey Joy Rodgers, Monica E. Cardella

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study focuses on characteristics of written feedback that influence students’ performance and confidence in addressing the mathematical complexity embedded in a Model-Eliciting Activity (MEA). MEAs are authentic mathematical modeling problems that facilitate students’ iterative development of solutions in a realistic context. We analyzed 132 first-year engineering students’ confidence levels and mathematical model scores on aMEA(pre and post feedback), along with teaching assistant feedback given to the students. The findings show several examples of affective and cognitive feedback that students reported that they used to revise their models. Students’ performance and confidence in developing mathematical models can be increased when …

Preparing Secondary Mathematics Teachers: Focus On Modeling In Algebra, Hyunyi Jung, Alexia Mintos, Jill Newton

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities. We also interviewed a group of three to four PSTs at each of the universities. We coded the interview transcripts using an analytic framework developed based on related literature and policy documents. We report the similarities and differences in perspectives among instructors and PSTs related to modeling at each university, along with …

Steam Flooding Screening And Eor Prediction By Using Clustering Algorithm And Data Visualization, Na Zhang

Masters Theses

"Enhanced Oil Recovery (EOR) techniques are vitally important in the oil industry because these techniques could not only extend the life of wells, but also produce 10% to 30% additional oil from the reservoir. However, selecting the most suitable EOR techniques for unknown reservoirs is not easy for decision making. Based on literature, EOR screening criteria could help to find the best candidates for unknown projects, which is classified into two categories: conventional EOR screening and advanced EOR screening. In this research, an artificial intelligent (AI) method, hierarchical clustering algorithm, is adapted to analyze both steam flooding projects and worldwide …

Uncertainty Quantification Of Turbulence Model Closure Coefficients For Transonic Wall-Bounded Flows, John Anthony Schaefer

Masters Theses

"The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-ω Model, and the …

Predicting Scenarios For Successful Autodissemination Of Pyriproxyfen By Malaria Vectors From Their Resting Sites To Aquatic Habitats; Description And Simulation Analysis Of A Field-Parameterizable Model, Samson Sifael Kiware, George F. Corliss, Stephen Merrill, Dickson W. Lwetoijera, Gregor J. Devine, Silas Majambere, Gerry F. Killeen

Electrical and Computer Engineering Faculty Research and Publications

Background

Large-cage experiments indicate pyriproxifen (PPF) can be transferred from resting sites to aquatic habitats by Anopheles arabiensis - malaria vector mosquitoes to inhibit emergence of their own offspring. PPF coverage is amplified twice: (1) partial coverage of resting sites with PPF contamination results in far higher contamination coverage of adult mosquitoes because they are mobile and use numerous resting sites per gonotrophic cycle, and (2) even greater contamination coverage of aquatic habitats results from accumulation of PPF from multiple oviposition events.

Methods and Findings

Deterministic mathematical models are described that use only field-measurable input parameters and capture the biological …

Mahalanobis Kernel-Based Support Vector Data Description For Detection Of Large Shifts In Mean Vector, Vu Nguyen

Electronic Theses and Dissertations

Statistical process control (SPC) applies the science of statistics to various process control in order to provide higher-quality products and better services. The K chart is one among the many important tools that SPC offers. Creation of the K chart is based on Support Vector Data Description (SVDD), a popular data classifier method inspired by Support Vector Machine (SVM). As any methods associated with SVM, SVDD benefits from a wide variety of choices of kernel, which determines the effectiveness of the whole model. Among the most popular choices is the Euclidean distance-based Gaussian kernel, which enables SVDD to obtain a …

Modeling The Dynamic Processes Of Challenge And Recovery (Stress And Strain) Over Time, Fan Yang

Department of Statistics: Dissertations, Theses, and Student Research

A dynamic process with challenge and recovery is an important branch in the family of stochastic processes. The dependent data of such processes are often observed over time, and hence, are time dependent. The purpose of this dissertation is to develop methods to characterize a dynamic process with challenge and recovery under different dimensionalities and error assumptions. In this dissertation, a univariate dynamic process under Gaussian assumption is discussed first and a bi-logistic model is developed by three different methods: compartment, additive, and Bayesian. Then the discussion is extended to a bivariate hysteresis system with challenge and recovery. Three methods: …

Diffuse Optical Measurements Of Head And Neck Tumor Hemodynamics For Early Prediction Of Chemo-Radiation Therapy Outcomes, Lixin Dong

Theses and Dissertations--Biomedical Engineering

Chemo-radiation therapy is a principal modality for the treatment of head and neck cancers, and its efficacy depends on the interaction of tumor oxygen with free radicals. In this study, we adopted a novel hybrid diffuse optical instrument combining a commercial frequency-domain tissue oximeter (Imagent) and a custom-made diffuse correlation spectroscopy (DCS) flowmeter, which allowed for simultaneous measurements of tumor blood flow and blood oxygenation. Using this hybrid instrument we continually measured tumor hemodynamic responses to chemo-radiation therapy over the treatment period of 7 weeks. We also explored monitoring dynamic tumor hemodynamic changes during radiation delivery. Blood flow data analysis …

Multi-State Models For Interval Censored Data With Competing Risk, Shaoceng Wei

Theses and Dissertations--Statistics

Multi-state models are often used to evaluate the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. In this dissertation, both multi-state Markov model and semi-Markov model are used to characterize the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk.

Firstly, a multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model …

Empirical Likelihood Confidence Band, Shihong Zhu

Theses and Dissertations--Statistics

The confidence band represents an important measure of uncertainty associated with a functional estimator and empirical likelihood method has been proved to be a viable approach to constructing confidence bands in many cases. Using the empirical likelihood ratio principle, this dissertation developed simultaneous confidence bands for many functions of fundamental importance in survival analysis, including the survival function, the difference and ratio of survival functions, the hazards ratio function, and other parameters involving residual lifetimes. Covariate adjustment was incorporated under the proportional hazards assumption. The proposed method can be very useful when, for example, an individualized survival function is desired …

New Results In Ell_1 Penalized Regression, Edward A. Roualdes

Theses and Dissertations--Statistics

Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate the variation of estimates – a notoriously difficult task for the …