Physical Sciences and Mathematics Commons^™

Probability Estimation In Random Forests, Chunyang Li

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Random Forests is a useful ensemble approach that provides accurate predictions for classification, regression and many different machine learning problems. Classification has been a very useful and popular application for Random Forests. However, it is preferable to have the probability of a membership rather than the simple knowledge that one belongs to whichever group. Votes and the regression method are current probability estimation methods that have been developed in Random Forests. In this thesis, we introduce two new methods, proximity weighting and the out-of-bag method, trying to improve the current methods. Several different simulations are designed to evaluate the new …

Empirical Properties Of Functional Regression Models And Application To High-Frequency Financial Data, Xi Zhang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Functional data analysis (FDA) has grown into a substantial field of statistical research, with new methodology, numerous useful applications and interesting novel theoretical developments. My dissertation focuses on the empirical properties of functional regression models and their application to financial data. We start from testing the empirical properties of forecasts with the functional autoregressive models based on simulated and real data. We define intraday returns and consider their prediction from such returns on a market index. This is an extension to intraday data of the Capital Asset Pricing model. Finally we investigate multifactor functional models and assess their suitability for …

Existence And Multiplicity Results On Standing Wave Solutions Of Some Coupled Nonlinear Schrodinger Equations, Rushun Tian

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Coupled nonlinear Schrodinger equations (CNLS) govern many physical phenomena, such as nonlinear optics and Bose-Einstein condensates. For their wide applications, many studies have been carried out by physicists, mathematicians and engineers from different respects. In this dissertation, we focused on standing wave solutions, which are of particular interests for their relatively simple form and the important roles they play in studying other wave solutions. We studied the multiplicity of this type of solutions of CNLS via variational methods and bifurcation methods.

Variational methods are useful tools for studying differential equations and systems of differential equations that possess the so-called variational …

Statistical Algorithms For Optimal Experimental Design With Correlated Observations, Chang Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The first part of my dissertation demonstrates that a modified simulated annealing algorithm can successfully determine highly efficient D-optimal designs for second order polynomial regression for a variety of correlated error structures.

In the second part, I solved weak universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size.

In the third part, we propose an improved Particle Swarm Optimization (PSO) algorithm with time varying parameters. Then combining the theorem of decision making and PSO, we innovated nested PSO …

Applications Of Bayesian Statistics In Fluvial Bed Load Transport, Mark L. Schmelter

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The science of fluvial sediment transport studies the processes involved in the movement of river sediments. It is commonly understood that when rivers flood they have a great capacity to move sand, gravel, and even larger cobbles and boulders. This process is not only limited to the big floods that usually attract so much attention, but also the more common river flows play a very important role in forming a river. As engineers and scientists, we like to be able to develop equations and relationships that describe some natural phenomenon—in this case, fluvial sediment transport. While we are able to …

Enhancement Of Random Forests Using Trees With Oblique Splits, Andrejus Parfionovas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Statistical classification is widely used in many areas where there is a need to make a data-driven decision, or to classify complicated cases or objects. For instance: disease diagnostics (is a patient sick or healthy, based on the blood test results?); weather forecasting (will there be a storm tomorrow, based on today's atmospheric pressure, air temperature, and wind velocity?); speech recognition (what was said over the phone, based on the caller's voice level and articulation); spam detection (can the unsolicited commercial e-mails be identified by their content?); and so on.

Classification trees …

Spatially Indexed Functional Data, Oleksandr Gromenko

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The increased concentration of greenhouse gases is associated with the global warming in the lower troposphere. For over twenty years, the space physics community has studied a hypothesis of global cooling in the thermosphere, attributable to greenhouse gases. While the global temperature increase in the lower troposphere has been relatively well established, the existence of global changes in the thermosphere is still under investigation.

A central difficulty in reaching definite conclusions is the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Time series of data that cover several decades exist only in a few separated (industrialized) …

Curds And Whey: Little Miss Muffit's Contribution To Multivariate Linear Regression, John Cameron Kidd

Undergraduate Honors Capstone Projects

A common multivariate statistical problem is the prediction of two or more response variables using two or more predictor variables. The simplest model for this situation is the multivariate linear regression model. The standard least squares estimation for this model involves regressing each response variable separately on all the predictor variables. Breiman and Friedman [1] show how to take advantage of correlations among the response variables to increase the predictive accuracy for each of the response variable with an algorithm they call Curds and Whey. In this report, I describe an implementation of the Curds and Whey algorithm in …