Digital Commons Network^™

Bayesian Methods In Analyzing The Diagnostic Accuracy\\ For Ordinal Ratings, Yun Yang

Theses and Dissertations

This dissertation focuses on ordinal classification ratings, which are commonly used in medical practice to assess the severity of a disease or condition. For example, a group of radiologists rate a set of mammograms and assign BI-RADS (Breast Imaging Reporting Data System) score for each mammogram. A Bayesian probit hierarchical model is first proposed to analyze this type of data. It links the ordinal ratings with both rater diagnostic skills and patient latent disease severity. Each rater diagnostic skills are quantified with two parameters, diagnostic bias and diagnostic magnifier. Patient latent disease severity is assumed to follow a different normal …

Statistical Inference Based On Elliptically Symmetric Distributions For Directional Data, Zehao Yu

Theses and Dissertations

Directional data arise in many scientific fields such as meteorology, oceanography, geology, zoology, and biomechanics. Geometrically, directional data lie in a spherical space. Although not in a spherical space, compositional data, such as microbiome data, can be mapped from a simplex to a spherical space via the component-wise square-root transformation. Other examples where compositional data emerge as a subject of interest include compositions of minerals in rocks, compositions of chemical mixtures, investment portfolios, and demographic composition of a population. This dissertation aims to develop inference procedures for analyzing directional data in general initially, with later focus shifted to the transformed …

Evaluation Of Factors Impacting Predictor Importance Results In Multilevel Models, Soonhwa (Suna) Paek

Theses and Dissertations

Background: Dominance Analysis (DA) was originally proposed to determine the relative importance of predictor variables in OLS regression models by comparing the change in model fit (i.e., R2) resulting from adding each predictor to each possible subset model (Azen & Budescu, 2003; Azen, 2013; Budescu, 1993). Although various educational studies show that DA can provide useful information in research, the DA procedure has not been studied extensively with Multilevel Linear Models (MLMs), which are commonly used to analyze nested data structures.

Purpose: This study aimed to identify appropriate multilevel measures of fit for the DA procedure in various MLMs, and …

Cte Induced Premium Principles And Properties, Linjiao Wu

Theses and Dissertations

The traditional pricing approach in the insurance industry assumes independence among insureds, yet overlooks the complexities of interdependent risk profiles. This dissertation addresses this limitation by proposing a premium pricing model tailored for managing dependent risks, drawing inspiration from conditional tail expectation (CTE) theory. In our model, each individual insured's premium is contingent upon the collective loss surpassing a predefined threshold.

To validate the efficacy of our model, we introduce several key properties to ensure fairness and stability in premium determination among insured individuals, including diversification and monotonicity. Diversification ensures that adding one policyholder to the insured group does not …

Robust-Efficient Fitting Of Loss Models Via Quantile Least Squares, Mohammed Adjei Adjieteh

Theses and Dissertations

Actuaries and statisticians use statistical models to predict future losses for pricing and other purposes. However, a key challenge in modeling is estimating the unknown parameters that index these distributions. Ensuring both efficiency and robustness of the chosen method is crucial, especially given the prevalence of outliers or extreme losses in insurance claims data. The primary objective of this dissertation is to introduce a robust, efficient, and computationally easy parameter estimation method that can be applied to various loss modeling scenarios. The proposed method exploits the joint asymptotic normality of sample quantiles (of i.i.d. random variables) to construct both ordinary …

A Spatial Decision Support System For Rent Estimation Of Retail Spaces In Manhattan Using Geographically Weighted Regression And Spatial Regression, Andie M. Migden Miller

Theses and Dissertations

This report outlines an automated, three-phase Spatial Decision Support System that creates models to estimate rent of retail spaces across Manhattan. First, enrich data with predictors. Second, optimize spatially aware neighborhood-level models by combining GWR, spatial regression, and non-spatial regression. Finally, visualize results in an Esri-based WebApp.

Markov Chain Model Of Three-Dimensional Daphnia Magna Movement, Helen L. Kafka

Theses and Dissertations

Daphnia magna make turns through an antennae-whipping action. This action occursevery few seconds, hence, during the intervening time, the animal either remains in place or continues movement roughly along its current course. We view their movement in three dimensions. We divide the movement in the three dimensions into the movement on a two-dimensional lattice and the movement between the different planes. For the movement on the lattice, we construct a second-order Markov chain model to make predictions about which region of the lattice the animal moves to based on where it was at the last two time points. The movement …

Utilizing Arma Models For Non-Independent Replications Of Point Processes, Lucas M. Fellmeth

Theses and Dissertations

The use of a functional principal component analysis (FPCA) approach for estimatingintensity functions from prior work allows us to obtain component scores of replicated point processes under the assumption of independent replications. We show these component scores can be modeled using classical autoregressive moving average (ARMA) models, thus allowing us to also apply the FPCA model to non-independent replications. The Divvy bike-sharing system in the city of Chicago is showcased as an application.

Bayesian Change Point Detection In Segmented Multi-Group Autoregressive Moving-Average Data For The Study Of Covid-19 In Wisconsin, Russell Latterman

Theses and Dissertations

Changepoint detection involves the discovery of abrupt fluctuations in population dynamics over time. We take a Bayesian approach to estimating points in time at which the parameters of an autoregressive moving average (ARMA) change, applying a Markov chain Monte Carlo method. We specifically assume that data may originate from one of two groups. We provide estimates of all multi-group parameters of a model of this form for both simulated and real-world data sets. We include a provision to resolve the problem of confounding ARMA parameter estimates and variance of segment data. We apply our model to identify points in time …

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

Developing Machine Learning And Time-Series Analysis Methods With Applications In Diverse Fields, Muhammed Aljifri

Theses and Dissertations

This dissertation introduces methodologies that combine machine learning models with time-series analysis to tackle data analysis challenges in varied fields. The first study enhances the traditional cumulative sum control charts with machine learning models to leverage their predictive power for better detection of process shifts, applying this advanced control chart to monitor hospital readmission rates. The second project develops multi-layer models for predicting chemical concentrations from ultraviolet-visible spectroscopy data, specifically addressing the challenge of analyzing chemicals with a wide range of concentrations. The third study presents a new method for detecting multiple changepoints in autocorrelated ordinal time series, using the …

Bayesian Estimation Of Hierarchical Linear Models From Incomplete Data: Cluster-Level Non-Linear Effects And Small Sample Sizes, Dongho Shin

Theses and Dissertations

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other nonlinear effects given small sample sizes, however, maximum likelihood estimation is suboptimal, and existing Gibbs samplers are based on a Bayesian joint distribution compatible with the HLM, but impute missing values of C by a Metropolis algorithm via a proposal density having a constant variance while the target …