Statistics and Probability Commons^™

Stat 380: Statistics And Applications, Yumou Qiu

UNL Faculty Course Portfolios

This portfolio prepares for the introduction level undergraduate statistic course (Stat 380) for the students with calculus background, which includes the course goals, contents as well as teaching methods for large session classes. Analysis and evaluation of student learning are also included. In-class activities and discussion helping students’ engagement are introduced. The homework is assigned by Canvas, which summaries the students’ solution and provides analysis for each student.

A Comparison Of Bridge Deterioration Models, Toktam Naderimoghaddam

College of Graduate Studies: Theses & Dissertations

Predicting how bridges will deteriorate is the key to budgeting financial and personnel resources. Deterioration models exist for specific components of a bridge, but no models exist for the sufficiency rating which is an overall measure of the condition and relevance of a bridge used for determining eligibility for federal funds.

We have 25 years worth of data collected by the Georgia Department of Transportation from 1992 to 2016 about all bridges in the State of Georgia. More precisely, each row in this data set includes the characteristics of each bridge along with the sufficiency rating of that bridge in …

Estimating The Optimal Cutoff Point For Logistic Regression, Zheng Zhang

Open Access Theses & Dissertations

Binary classification is one of the main themes of supervised learning. This research is concerned about determining the optimal cutoff point for the continuous-scaled outcomes (e.g., predicted probabilities) resulting from a classifier such as logistic regression. We make note of the fact that the cutoff point obtained from various methods is a statistic, which can be unstable with substantial variation. Nevertheless, due partly to complexity involved in estimating the cutpoint, there has been no formal study on the variance or standard error of the estimated cutoff point.

In this Thesis, a bootstrap aggregation method is put forward to estimate the …

Backward Elimination Algorithm For High Dimensional Variable Screening, Sophia Korkor Foli

Open Access Theses & Dissertations

In recent times, variable selection in high-dimensional data has become a challenging prob- lem. We investigate here a popular but classical variable screening method, the Back- ward Elimination (BE) in a high dimensional setup (small-n-large P). The BE method as a variable screening method reduces the dimension of small-n-large P data into a lower dimensional data and then established shrinkage methods such as: LASSO, SCAD and MCP can be applied directly. To overcome the problems in high dimensional data, Chen and Chen (2008) recently developed a family of Extended Bayesian Information Criterion (EBIC) which is consistent with finite sample properties …

Extraction Of Fiber Morphology From Sem Images For Quality Control Of Fiber Reinforced Composites Manufacturing, Md Fashiar Rahman

Open Access Theses & Dissertations

The morphology of fibers (e.g. spatial uniformity, orientation, and length) plays a decisive role in determining the material properties or fabrication quality of fiber-reinforced nanocomposites. Hence, determining the morphology becomes a very critical issue in the field of nanocomposite quality control. The conventional way of quality inspection is to take the scanning electron microscopic (SEM) images of the cross-section of composite material and do the visual checking of these SEM images to evaluate the nanofiber alignment and length distribution. But this type of inspection is often subjective, inaccurate and time consuming. Moreover, the extremely small size of nanofibers makes the …

How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer

Mathematics and Statistics: Faculty Publications and Other Works

Statistical applications in sports have long centered on how to best separate signal (e.g., team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season and game-to-game variability of team …

How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer

Mathematics and Statistics: Faculty Publications and Other Works

Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript, we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season, and game-to-game variability of team …

Comparing Various Machine Learning Statistical Methods Using Variable Differentials To Predict College Basketball, Nicholas Bennett

Williams Honors College, Honors Research Projects

The purpose of this Senior Honors Project is to research, study, and demonstrate newfound knowledge of various machine learning statistical techniques that are not covered in the University of Akron’s statistics major curriculum. This report will be an overview of three machine-learning methods that were used to predict NCAA Basketball results, specifically, the March Madness tournament. The variables used for these methods, models, and tests will include numerous variables kept throughout the season for each team, along with a couple variables that are used by the selection committee when tournament teams are being picked. The end goal is to find …

Introductory Statistics, Barbara Illowsky, Susan Dean

Open Access Textbooks

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.

Examining The Confirmatory Tetrad Analysis (Cta) As A Solution Of The Inadequacy Of Traditional Structural Equation Modeling (Sem) Fit Indices, Hangcheng Liu

Theses and Dissertations

Structural Equation Modeling (SEM) is a framework of statistical methods that allows us to represent complex relationships between variables. SEM is widely used in economics, genetics and the behavioral sciences (e.g. psychology, psychobiology, sociology and medicine). Model complexity is defined as a model’s ability to fit different data patterns and it plays an important role in model selection when applying SEM. As in linear regression, the number of free model parameters is typically used in traditional SEM model fit indices as a measure of the model complexity. However, only using number of free model parameters to indicate SEM model complexity …

Fact Sheet, Yale University Office Of Institutional Research

Fact Sheets

No abstract provided.

Complex-Valued Time Series Modeling For Improved Activation Detection In Fmri Studies, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we …

On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Wenhui Sheng, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.

A Proposed Taxonomy For The Systems Statistical Engineering Body Of Knowledge, Teddy Steven Cotter

Engineering Management & Systems Engineering Faculty Publications

In the ASEM-IAC 2012, Cotter (2012) identified the gaps in knowledge that statistical engineering needs to address, explored additional gaps in knowledge not addressed in the prior works, and set forth a working definition of and body of knowledge for statistical engineering. In the ASEM-IAC 2015, Cotter (2015) proposed a systemic causal Bayesian hierarchical model that addressed the knowledge gap needed to integrate deterministic mathematical engineering causal models within a stochastic framework. Missing, however, is the framework for specifying the hierarchical qualitative systems structures necessary and sufficient for specifying systemic causal Bayesian hierarchical models. In the ASEM-IAC 2016, Cotter (2016) …

Some New And Generalized Distributions Via Exponentiation, Gamma And Marshall-Olkin Generators With Applications, Hameed Abiodun Jimoh

College of Graduate Studies: Theses & Dissertations

Three new generalized distributions developed via completing risk, gamma generator, Marshall-Olkin generator and exponentiation techniques are proposed and studied. Structural properties including quantile functions, hazard rate functions, moment, conditional moments, mean deviations, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates are presented. Monte Carlo simulation is employed to examine the performance of the proposed distributions. Applications of the generalized distributions to real lifetime data are presented to illustrate the usefulness of the models.

Adaptive Methods For Point Cloud And Mesh Processing, Zinat Afrose

Computational Modeling & Simulation Engineering Theses & Dissertations

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data.

The major …

Non-Linear Machine Learning With Active Sampling For Mox Drift Compensation, Tamara Matthews, Muhammad Iqbal, Horacio Gonzalez-Velez

Conference papers

Abstract—Metal oxide (MOX) gas detectors based on SnO2 provide low-cost solutions for real-time sensing of complex gas mixtures for indoor ambient monitoring. With high sensitivity under ideal conditions, MOX detectors may have poor longterm response accuracy due to environmental factors (humidity and temperature) along with sensor aging, leading to calibration drifts. Finding a simple and efficient solution to correct such calibration drifts has been the subject of numerous studies but remains an open problem. In this work, we present an efficient approach to MOX calibration using active and transfer sampling techniques coupled with non-linear machine learning algorithms, namely neural networks, …

The Use Of Item Response Theory In Survey Methodology: Application In Seat Belt Data, Mark K. Ledbetter, Norou Diawara, Bryan E. Porter

Mathematics & Statistics Faculty Publications

Problem: Several approaches to analyze survey data have been proposed in the literature. One method that is not popular in survey research methodology is the use of item response theory (IRT). Since accurate methods to make prediction behaviors are based upon observed data, the design model must overcome computation challenges, but also consideration towards calibration and proficiency estimation. The IRT model deems to be offered those latter options. We review that model and apply it to an observational survey data. We then compare the findings with the more popular weighted logistic regression. Method: Apply IRT model to the observed data …

Decoupled, Linear, And Energy Stable Finite Element Method For The Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, Yali Gao, Xiaoming He, Liquan Mei, Xiaofeng Yang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we consider the numerical approximation for a phase field model of the coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn—Hilliard—Navier—Stokes equations in the free flow region and Cahn—Hilliard—Darcy equations in the porous media region that are coupled by seven interface conditions. The coupled system is decoupled based on the interface conditions and the solution values on the interface from the previous time step. A fully discretized scheme with finite elements for the spatial discretization is developed to solve the decoupled system. In order to deal with the difficulties arising from the …

Spatiotemporal Variations In Coexisting Multiple Causes Of Death And The Associated Factors, Emmanuel Oluwatobi Salawu

Walden Dissertations and Doctoral Studies

The study and practice of epidemiology and public health benefit from the use of mortality statistics, such as mortality rates, which are frequently used as key health indicators. Furthermore, multiple causes of death (MCOD) data offer important information that could not possibly be gathered from other mortality data. This study aimed to describe the interrelationships between various causes of death in the United States in order to improve the understanding of the coexistence of MCOD and thereby improve public health and enhance longevity. The social support theory was used as a framework, and multivariate linear regression analyses were conducted to …