Statistical Models Commons^™

Modeling Mean And Variability Of Anxiety In Ecological Momentary Assessment Data Using Mixed-Effects Location–Scale Models, Trenzy Odero

Electronic Theses and Dissertations

Ecological Momentary Assessment is a method of collecting repeated measures of people in real time within natural environments. This results in hierarchical data that has a significant amount of variation at the person level. The traditional linear mixedeffects models assume that the residual variance is constant, which might not be true when the residual variance varies among individuals as well as in time. This thesis uses mixed-effects location-scale (MELS) models to model the mean and variance of an EMA outcome together. By introducing the possibility of variability in residual variance within and across individuals and with covariates, the MELS framework …

A Leslie System For A Demographic Simulation: From An Actuarial Point Of View, David Kings

Electronic Theses and Dissertations

This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival …

Exploring The Diagnostic Potential Of Radiomics-Based Pet Image Analysis For T-Stage Tumor Diagnosis, Victor Aderanti

Electronic Theses and Dissertations

Cancer is a leading cause of death globally, and early detection is crucial for better

outcomes. This research aims to improve Region Of Interest (ROI) segmentation

and feature extraction in medical image analysis using Radiomics techniques

with 3D Slicer, Pyradiomics, and Python. Dimension reduction methods, including

PCA, K-means, t-SNE, ISOMAP, and Hierarchical Clustering, were applied to highdimensional features to enhance interpretability and efficiency. The study assessed the ability of the reduced feature set to predict T-staging, an essential component of the TNM system for cancer diagnosis. Multinomial logistic regression models were developed and evaluated using MSE, AIC, BIC, and Deviance …

Landslide Susceptibility And Tree Ring Eccentricity Analysis Along Unstable Slopes Of The New River Watershed, Anderson And Morgan Counties, Tn, Megan Palmer

Electronic Theses and Dissertations

Landslides are mass movements that affect infrastructure across East Tennessee, causing problems for the Tennessee Department of Transportation (TDOT). An assessment of conditions and locations of unstable slopes can aid TDOT in infrastructure management. Landslide susceptibility was evaluated for Anderson and Morgan counties, TN, off State Route 116 in the New River watershed. Susceptibility maps used a landslide inventory and six factors: elevation, slope, geology, distance from stream, rainfall, and curvature, input in forest-based classification and logistic regression models. Additionally, affected trees along these unstable slopes in Anderson and Morgan counties were cored to analyze mass movement impacts on tree …

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

Proteomics And Machine Learning For Pulmonary Embolism Risk With Protein Markers, Yaa Amankwah Awuah

Electronic Theses and Dissertations

This thesis investigates protein markers linked to pulmonary embolism risk using proteomics and statistical methods, employing unsupervised and supervised machine learning techniques. The research analyzes existing datasets, identifies significant features, and observes gender differences through MANOVA. Principal Component Analysis reduces variables from 378 to 59, and Random Forest achieves 70% accuracy. These findings contribute to our understanding of pulmonary embolism and may lead to diagnostic biomarkers. MANOVA reveals significant gender differences, and applying proteomics holds promise for clinical practice and research.

Finding A Representative Distribution For The Tail Index Alpha, Α, For Stock Return Data From The New York Stock Exchange, Jett Burns

Electronic Theses and Dissertations

Statistical inference is a tool for creating models that can accurately display real-world events. Special importance is given to the financial methods that model risk and large price movements. A parameter that describes tail heaviness, and risk overall, is α. This research finds a representative distribution that models α. The absolute value of standardized stock returns from the Center for Research on Security Prices are used in this research. The inference is performed using R. Approximations for α are found using the ptsuite package. The GAMLSS package employs maximum likelihood estimation to estimate distribution parameters using the CRSP data. The …

Robustness Of Semi-Parametric Survival Model: Simulation Studies And Application To Clinical Data, Isaac Nwi-Mozu

Electronic Theses and Dissertations

An efficient way of analyzing survival clinical data such as cancer data is a great concern to health experts. In this study, we investigate and propose an efficient way of handling survival clinical data. Simulation studies were conducted to compare performances of various forms of survival model techniques using an R package ``survsim". Models performance was conducted with varying sample sizes as small ($n5000$). For small and mild samples, the performance of the semi-parametric outperform or approximate the performance of the parametric model. However, for large samples, the parametric model outperforms the semi-parametric model. We compared the effectiveness and reliability …

Distribution Of A Sum Of Random Variables When The Sample Size Is A Poisson Distribution, Mark Pfister

Electronic Theses and Dissertations

A probability distribution is a statistical function that describes the probability of possible outcomes in an experiment or occurrence. There are many different probability distributions that give the probability of an event happening, given some sample size n. An important question in statistics is to determine the distribution of the sum of independent random variables when the sample size n is fixed. For example, it is known that the sum of n independent Bernoulli random variables with success probability p is a Binomial distribution with parameters n and p: However, this is not true when the sample size …

Geostatistical Analysis Of Potential Sinkhole Risk: Examining Spatial And Temporal Climate Relationships In Tennessee And Florida, Kimberly Blazzard

Electronic Theses and Dissertations

Sinkholes are a significant hazard for the southeastern United States. Although differences in climate are known to affect karst environments differently, quantitative analyses correlating sinkhole formation with climate variables is lacking. A temporal linear regression for Florida sinkholes and two modeled regressions for Tennessee sinkholes were produced: a general linearized logistic regression and a MaxEnt derived species distribution model. Temporal results showed highly significant correlations with precipitation, teleconnection patterns, temperature, and CO₂, while spatial results showed highly significant correlations with precipitation, wind speed, solar radiation, and maximum temperature. Regression results indicated that some sinkhole formation variability could be …

Performance Of Imputation Algorithms On Artificially Produced Missing At Random Data, Tobias O. Oketch

Electronic Theses and Dissertations

Missing data is one of the challenges we are facing today in modeling valid statistical models. It reduces the representativeness of the data samples. Hence, population estimates, and model parameters estimated from such data are likely to be biased.

However, the missing data problem is an area under study, and alternative better statistical procedures have been presented to mitigate its shortcomings. In this paper, we review causes of missing data, and various methods of handling missing data. Our main focus is evaluating various multiple imputation (MI) methods from the multiple imputation of chained equation (MICE) package in the statistical software …

A Multi-Indexed Logistic Model For Time Series, Xiang Liu

Electronic Theses and Dissertations

In this thesis, we explore a multi-indexed logistic regression (MILR) model, with particular emphasis given to its application to time series. MILR includes simple logistic regression (SLR) as a special case, and the hope is that it will in some instances also produce significantly better results. To motivate the development of MILR, we consider its application to the analysis of both simulated sine wave data and stock data. We looked at well-studied SLR and its application in the analysis of time series data. Using a more sophisticated representation of sequential data, we then detail the implementation of MILR. We compare …

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

Electronic Theses and Dissertations

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

Electronic Theses and Dissertations

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial …

Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker

Electronic Theses and Dissertations

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …

Some New Probability Distributions Based On Random Extrema And Permutation Patterns, Jie Hao

Electronic Theses and Dissertations

In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X₁,X₂, ..., X_N, where each X_i has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where X_i is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

A Singular Perturbation Approach To The Fitzhugh-Nagumo Pde For Modeling Cardiac Action Potentials., Jeremy Brooks

Undergraduate Honors Theses

The study of cardiac action potentials has many medical applications. Dr. Dennis Noble first used mathematical models to study cardiac action potentials in the 1960s. We begin our study of cardiac action potentials with one form of the Fitzhugh-Nagumo partial differential equation. We use the non-classical method to produce a closed form solution for the decoupled Fitzhugh Nagumo equation. Using voltage recording data of action potentials in a cardiac myocyte and in purkinje fibers, we estimate parameter values for the closed form solution with standard linear and non-linear regression methods. Results are limited, thus leading us to perturb the solution …