Statistics and Probability Commons^™

A Rotatable Asymmetric Variable Compensation Mirt Model, Xinchu Zhao

Theses and Dissertations

The purpose of this study is to develop, estimate, and interpret a new variable compensation multidimensional item response theory (MIRT) model, named the Rotatable Asymmetric Variable Compensation Model (RAVCM), that allows for transformation between different correlation structures. Since the model is rotatable like the common compensatory models (CM), it is not necessary to specify or estimate the correlation of abilities to recover the model. Also, it can approximate the existing MIRT models well. In simulation, the RAVCM is shown to estimate the parameters with small error, especially when the non-compensatory model (NCM) is the true model and the correlation of …

Discovery Of Community Structures In Static And Dynamic Networks, Shiwen Shen

Theses and Dissertations

With the development of computer technology, researchers are able to observe and collect enormous amount of data, where the independent and identical distributed assumption is violated. For example, in sociology, individuals in an organization interact with each other to change the underlying social structure; in biology, understanding the gene-gene interaction helps researchers to detect potential diseases; in politics, voters are mutually influenced before the election via private/public speeches and parades, which might ultimately change the election results. It is crucial to study how individuals interact with each other from the data, which would lead to tremendous contributions to the society. …

Semiparametric Regression In The Presence Of Measurement Error, Xiang Li

Theses and Dissertations

The error-in-covariates problem has received great attention among researchers who study semiparametric and nonparametric inference for regression models over the past two decades. Without correcting for the measurement error in covariates, estimators for covariate effect usually contain bias. To account for measurement error, much research have been done in mean regression (Liang et al., 1999; Fuller, 2009; Carroll et al., 2006) and quantile regression (He and Liang, 2000; Hardle et al., 2000; Wei and Carroll, 2009). In contrast, there is little research in mode regression and this motivates us to propose semiparametric methods to address this error-incovariates problem in Chapters …

Mechanism Design, Matching Theory And The Stable Roommates Problem, Yashaswi Mohanty

Honors Theses

This thesis consists of two independent albeit related chapters. The first chapter introduces concepts from mechanism design and matching theory, and discusses potential applications of this theory, particularly in relation to dorm allocations in colleges. The second chapter investigates a subset of the dorm allocation problem, namely that of matching roommates. In particular, the paper looks at the probability of solvability of random instances of the stable roommates game under the condition that preferences are not completely random and exogenous but endogenously determined through a dependence on room choice. These probabilities are estimated using Monte-Carlo simulations and then compared with …

A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam

Department of Math & Statistics Faculty Publications

The TV game show “The Price is Right” features a bidding auction called “Contestants’ Row” that rewards the player (out of 4) who bids closest to an item’s value, without overbidding. This paper considers ways in which players can maximize a winning probability based on the player's bidding order. We consider marginal strategies in which players assume opponents are bidding individually perceived values of the merchandise. Based on preceding bids of others, players have information available to create strategies. We consider conditional strategies in which players adjust bids knowing other players are using strategies. The last bidder has a large …

Step-Selection Functions For Modeling Animal Movement -- Case Study: African Buffalo, Maia Adar

CMC Senior Theses

Understanding what factors influence wildlife movement allows landscape planners to make informed decisions that benefit both animals and humans. New quantitative methods, such as step-selection functions, provide valuable objective analyses of wildlife connectivity. This paper provides a framework for creating a step-selection function and demonstrates its use in a case study. The first section provides a general introduction about wildlife connectivity research. The second section explains the math behind the step-selection function using a simple example. The last section gives the results of a step-selection model for African buffalo in the Kavango Zambezi Transfrontier Conservation Area. Buffalo were found to …

Predictive Golf Analytics Versus The Daily Fantasy Sports Market, John O'Malley

CMC Senior Theses

This study examines the different skills necessary for PGA tour players to succeed at specific annual tournaments, in order to create a predictive model for DraftKings PGA contests. The model takes into account data from the PGA Tour ShotLink Intelligence Program. The predictive model is created each week based on past results from the specific tournament in question, with the hope of predicting a group of twenty-five players who should be successful based on their statistical profile. The results of the model are detailed in this paper, which covers the first nine weeks of the 2017 PGA Tour season, with …

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iii, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work may be a source of preventing reinventing and duplicating the existing distributions and calling them newly proposed distributions.

On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.

On Characterizations Of Mcllog, Ellogw, Pthl And K-Ge Distributions, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

Huang S. and Oluyede (2016), Oluyede et al. (2016), Krishnarani (2016) and Rather and Rather (2017) consider the "McDonald Log-Logistic", the "Exponentiated Log-Logistic Weibull", the "Power Transformation Half-Logistic" and "k-Generalized Exponential" distributions, respectively, and study certain properties and applications of these distributions. The present short note is intended to complete, in some way, the above mentioned works via establishing certain characterizations of these distributions in different directions.

A Bayesian Variable Selection Approach Yields Improved Detection Of Brain Activation From Complex-Valued Fmri, Cheng-Han Yu, Raquel Prado, Hernando Ombao, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation …

Analyzing Sensor Based Human Activity Data Using Time Series Segmentation To Determine Sleep Duration, Yogesh Deepak Lad

Masters Theses

"Sleep is the most important thing to rest our brain and body. A lack of sleep has adverse effects on overall personal health and may lead to a variety of health disorders. According to Data from the Center for disease control and prevention in the United States of America, there is a formidable increase in the number of people suffering from sleep disorders like insomnia, sleep apnea, hypersomnia and many more. Sleep disorders can be avoided by assessing an individual's activity over a period of time to determine the sleep pattern and duration. The sleep pattern and duration can be …

Statistics And Biomechanics: An Interdisciplinary Evaluation Of The Mathematical, Practical, And Athletic Applications Of Principal Component Analysis, Sydney Grace Davis

Undergraduate Honors Theses

Excerpt from Introduction

Coaches and athletes around the world are in constant pursuit of improving their athletic performance. For some, a routine amount of weight lifting, cardiovascular exercise, agilities and flexibility training with gradual advancement may be enough to see growth. However, many are not satisfied and turn to in-depth analyses of their techniques in order to measure their progress. After an intense workout or competition, coaches spend time breaking down athletic performances based on major movements. By compartmentalizing these activities, they can identify which motions are efficient and which ones hinder fluid motion. From this evaluation and discernment, athletes …

Categorizing A Continuous Predictor Subject To Measurement Error, Betsabé G. Blas Achic, Tianying Wang, Ya Su, Victor Kipnis, Kevin Dodd, Raymond J. Carroll

Statistics Faculty Publications

Epidemiologists often categorize a continuous risk predictor, even when the true risk model is not a categorical one. Nonetheless, such categorization is thought to be more robust and interpretable, and thus their goal is to fit the categorical model and interpret the categorical parameters. We address the question: with measurement error and categorization, how can we do what epidemiologists want, namely to estimate the parameters of the categorical model that would have been estimated if the true predictor was observed? We develop a general methodology for such an analysis, and illustrate it in linear and logistic regression. Simulation studies are …

Time Dependent Attribute-Level Best Worst Discrete Choice Modelling, Amanda Working, Mohammed Alqawba, Norou Diawara, Ling Li

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in statistical modelling of consumer behavior. Such models are used in many areas including social sciences, health economics, transportation research, and health systems research and they are time dependent. In this manuscript, we review references on the study of such models, develop DCMs with emphasis on time dependent best-worst choice and discrimination between choice attributes. Referenced measurements of the dynamic DCMs are simulated. Expected utilities over time are derived using Markov decision processes. We study attributes and attribute-levels associated with the quality of life of seniors, report the estimation results, and discuss our findings.

Microrna Expression Patterns In Human Anterior Cingulate And Motor Cortex: A Study Of Dementia With Lewy Bodies Cases And Controls, Peter T. Nelson, Wang-Xia Wang, Sarah A. Janse, Katherine L. Thompson

Sanders-Brown Center on Aging Faculty Publications

Overview

MicroRNAs (miRNAs) have been implicated in neurodegenerative diseases including Parkinson’s disease and Alzheimer’s disease (AD). Here, we evaluated the expression of miRNAs in anterior cingulate (AC; Brodmann area [BA] 24) and primary motor (MO; BA 4) cortical tissue from aged human brains in the University of Kentucky AD Center autopsy cohort, with a focus on dementia with Lewy bodies (DLB).

Methods

RNA was isolated from gray matter of brain samples with pathology-defined DLB, AD, AD+DLB, and low-pathology controls, with n=52 cases initially included (n=23 with DLB), all with low (<4hrs) postmortem intervals. RNA was profiled using Exiqon miRNA microarrays. Quantitative PCR for post-hoc replication was performed on separate cases (n=6 controls) and included RNA isolated from gray matter of MO, AC, primary somatosensory (BA 3), and dorsolateral prefrontal (BA 9) cortical regions.

Results

The miRNA expression patterns differed substantially according to …

Automated Tree-Level Forest Quantification Using Airborne Lidar, Hamid Hamraz

Theses and Dissertations--Computer Science

Traditional forest management relies on a small field sample and interpretation of aerial photography that not only are costly to execute but also yield inaccurate estimates of the entire forest in question. Airborne light detection and ranging (LiDAR) is a remote sensing technology that records point clouds representing the 3D structure of a forest canopy and the terrain underneath. We present a method for segmenting individual trees from the LiDAR point clouds without making prior assumptions about tree crown shapes and sizes. We then present a method that vertically stratifies the point cloud to an overstory and multiple understory tree …

Modeling And Mapping Location-Dependent Human Appearance, Zachary Bessinger

Theses and Dissertations--Computer Science

Human appearance is highly variable and depends on individual preferences, such as fashion, facial expression, and makeup. These preferences depend on many factors including a person's sense of style, what they are doing, and the weather. These factors, in turn, are dependent upon geographic location and time. In our work, we build computational models to learn the relationship between human appearance, geographic location, and time. The primary contributions are a framework for collecting and processing geotagged imagery of people, a large dataset collected by our framework, and several generative and discriminative models that use our dataset to learn the relationship …

Occurrence And Attributes Of Two Echinoderm-Bearing Faunas From The Upper Mississippian (Chesterian; Lower Serpukhovian) Ramey Creek Member, Slade Formation, Eastern Kentucky, U.S.A., Ann Well Harris

Theses and Dissertations--Earth and Environmental Sciences

Well-preserved echinoderm faunas are rare in the fossil record, and when uncovered, understanding their occurrence can be useful in interpreting other faunas. In this study, two such faunas of the same age from separate localities in the shallow-marine Ramey Creek Member of the Slade Formation in the Upper Mississippian (Chesterian) rocks of eastern Kentucky are examined. Of the more than 5,000 fossil specimens from both localities, only 9–34 percent were echinoderms from 3–5 classes. Nine non-echinoderm (8 invertebrate and one vertebrate) classes occurred at both localities, but of these, bryozoans, brachiopods and sponges dominated. To understand the attributes of both …

High Dimensional Multivariate Inference Under General Conditions, Xiaoli Kong

Theses and Dissertations--Statistics

In this dissertation, we investigate four distinct and interrelated problems for high-dimensional inference of mean vectors in multi-groups.

The first problem concerned is the profile analysis of high dimensional repeated measures. We introduce new test statistics and derive its asymptotic distribution under normality for equal as well as unequal covariance cases. Our derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. We also derive consistent and unbiased estimators of the asymptotic variances for equal and unequal covariance cases respectively.

The second problem considered is the accurate inference for high-dimensional repeated …