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 …

Comparing Group Means When Nonresponse Rates Differ, Gabriela M. Stegmann

UNF Graduate Theses and Dissertations

Missing data bias results if adjustments are not made accordingly. This thesis addresses this issue by exploring a scenario where data is missing at random depending on a covariate x. Four methods for comparing groups while adjusting for missingness are explored by conducting simulations: independent samples t-test with predicted mean stratification, independent samples t-test with response propensity stratification, independent samples t-test with response propensity weighting, and an analysis of covariance. Results show that independent samples t-test with response propensity weighting and analysis of covariance can appropriately adjust for bias. ANCOVA is the stronger method 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 …

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 …

Statistical Engineering: A Causal-Stochastic Modeling Research Update, Teddy Steven Cotter

Engineering Management & Systems Engineering Faculty Publications

In the ASEM-IAC 2012, Cotter (2012) summarized prior works that led to the proposal for statistical engineering, identified the gaps in knowledge that statistical engineering needs to address, explored additional gaps in knowledge not addressed in the prior works, set forth a working definition of and body of knowledge for statistical engineering, and set forth proposals of potential systems contributions the Engineering Management profession could make toward the development of statistical engineering. In 2014, the ASQ Statistics Division, DOT&E, NASA, and IDA co-sponsored a Statistical Engineering Agreement to jointly research development of the discipline of statistical engineering. The statistics community …

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 …

Developments In Nonparametric Regression Methods With Application To Raman Spectroscopy Analysis, Jing Guo

Theses and Dissertations--Epidemiology and Biostatistics

Raman spectroscopy has been successfully employed in the classification of breast pathologies involving basis spectra for chemical constituents of breast tissue and resulted in high sensitivity (94%) and specificity (96%) (Haka et al, 2005). Motivated by recent developments in nonparametric regression, in this work, we adapt stacking, boosting, and dynamic ensemble learning into a nonparametric regression framework with application to Raman spectroscopy analysis for breast cancer diagnosis. In Chapter 2, we apply compound estimation (Charnigo and Srinivasan, 2011) in Raman spectra analysis to classify normal, benign, and malignant breast tissue. We explore both the spectra profiles and their derivatives to …

Nonlinear Hierarchical Models For Longitudinal Experimental Infection Studies, Michael David Singleton

Theses and Dissertations--Epidemiology and Biostatistics

Experimental infection (EI) studies, involving the intentional inoculation of animal or human subjects with an infectious agent under controlled conditions, have a long history in infectious disease research. Longitudinal infection response data often arise in EI studies designed to demonstrate vaccine efficacy, explore disease etiology, pathogenesis and transmission, or understand the host immune response to infection. Viral loads, antibody titers, symptom scores and body temperature are a few of the outcome variables commonly studied. Longitudinal EI data are inherently nonlinear, often with single-peaked response trajectories with a common pre- and post-infection baseline. Such data are frequently analyzed with statistical methods …

Sobriety In Delta Not Sober, Joe Mashburn

Mathematics Faculty Publications

We will show that the space delta not sober defined by Coecke and Martin is sober in the Scott topology, but not in the weakly way below topology.

The Bootstrap Estimation In Time Series, Yun Liu

Dissertations, Master's Theses and Master's Reports

Time series, a special case in dependent data sequence, is widely used in many fields. In time series, linear process models are quite popularly used. General form of linear process indicates the time dependence property of time series, AR(p), MA(q) and ARMA(p;,q) models are all linear process models. In this report, simulations are based on the simplest models of these linear process models, such as AR(1), MA(1) and ARMA(1,1) models. AR(1)-SEASON, which is developed based on AR(1) model by changing the weight of residuals, is also considered in this report. To deal with dependent data sequence, common methods which aim …

Evaluating The Long-Term Effects Of Logging Residue Removals In Great Lakes Aspen Forests, Michael I. Premer

Dissertations, Master's Theses and Master's Reports

Commercial aspen (Populus spp.) forests of the Great Lakes region are primarily managed for timber products such as pulp fiber and panel board, but logging residues (topwood and non-merchantable bolewood) are potentially important for utilization in the bioenergy market. In some regions, pulp and paper mills already utilize residues as fuel in combustion for heat and electricity, and progressive energy policies will likely cause an increase in biomass feedstock demand. The effects of removing residues, which have a comparatively high concentration of macronutrients, is poorly understood when evaluating long-term site productivity, future timber yields, plant diversity, stand dynamics, and …

Estimation And Identification Of Change Points In Panel Models With Nonstationary Or Stationary Regressors And Error Term, Badi H. Baltagi, Chihwa Kao, Long Liu

Center for Policy Research

This paper studies the estimation of change point in panel models. We extend Bai (2010) and Feng, Kao and Lazarová (2009) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered.

Taming The Hurricane Of Acquisition Cost Growth – Or At Least Predicting It, Allen J. Deneve, Erin T. Ryan, Jonathan D. Ritschel, Christine M. Schubert Kabban

Faculty Publications

Cost growth is a persistent adversary to efficient budgeting in the Department of Defense. Despite myriad studies to uncover causes of this cost growth, few of the proposed remedies have made a meaningful impact. A key reason may be that DoD cost estimates are formulated using the highly unrealistic assumption that a program’s current baseline characteristics will not change in the future. Using a weather forecasting analogy, the authors demonstrate how a statistical approach may be used to account for these inevitable baseline changes and identify related cost growth trends. These trends are then used to reduce the error in …

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 …

Unavoidable Minors Of Large 4-Connected Bicircular Matroids, Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.

Using Time Series Models For Defect Prediction In Software Release Planning, James W. Tunnell

All Master's Theses

To produce a high-quality software release, sufficient time should be allowed for testing and fixing defects. Otherwise, there is a risk of slip in the development schedule and/or software quality. A time series model is used to predict the number of bugs created during development. The model depends on the previous numbers of bugs created. The model also depends, in an exogenous manner, on the previous numbers of new features resolved and improvements resolved. This model structure would allow hypothetical release plans to be compared by assessing their predicted impact on testing and defect- fixing time. The VARX time series …

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.