Probability Commons^™

Predicting Diabetes Diagnoses, Sarah Netchert

Student Research Poster Presentations 2020

This study explored the traits and health state of African Americans in central Virginia in order to determine what traits put people at a higher probability of being diagnosed with diabetes. We also want to know which traits will generate the highest probability a person will be diagnosed with diabetes. Traits that were included and used in this study were cholesterol, stabilized glucose, high density lipoprotein levels, age(years), gender, height(inches), weight(pounds), systolic blood pressure, diastolic blood pressure, waist size(inches), and hip size(inches). There were 403 individuals included in study since they were only ones screened for diabetes out of 1,046 …

Shrinkage Priors For Isotonic Probability Vectors And Binary Data Modeling, Philip S. Boonstra, Daniel R. Owen, Jian Kang

The University of Michigan Department of Biostatistics Working Paper Series

This paper outlines a new class of shrinkage priors for Bayesian isotonic regression modeling a binary outcome against a predictor, where the probability of the outcome is assumed to be monotonically non-decreasing with the predictor. The predictor is categorized into a large number of groups, and the set of differences between outcome probabilities in consecutive categories is equipped with a multivariate prior having support over the set of simplexes. The Dirichlet distribution, which can be derived from a normalized cumulative sum of gamma-distributed random variables, is a natural choice of prior, but using mathematical and simulation-based arguments, we show that …

How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller

CMC Senior Theses

In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …

Chase-Escape On Sparse Networks, Emma Sylvie Bernstein

Senior Projects Spring 2020

Chase-escape is a competitive growth process in which prey spread through an environment while being chased and consumed by predators. The environment is typically modeled by a graph—such as a lattice, tree, or clique—and the species by particles competing to occupy sites. It is arguably more natural to study these dynamics in heterogeneous environments. To this end, we consider chase-escape on a canonical sparse random graph called the Erdo ̋s-R ́enyi graph. We show that if prey spreads too slowly then both species quickly die out. On the other hand, if prey spreads fast enough, then coexistence occurs. Concrete bounds …

Time-Dependent Reliability Framework For Durability Design Of Frp Composites, Rajneesh Kumar Bharil

Graduate Theses, Dissertations, and Problem Reports

The life-cycle performance, durability, and aging characteristics of Fiber Reinforced Polymer (FRP or Structural Composites) have been of keen interest to the engineers engaged in the FRP design, construction, and manufacturing. Unlike conventional construction materials such as steel and concrete, the design guidelines to account for the aging of FRP are somewhat scattered or not available in an approved or consistent format. Loss of strength over time or aging of any structural material should be of concern to engineers as the in-service lifespan of many engineering structures is expected to exceed 100 years. Use of durability strength-reduction factors or factors …

V-Slam And Sensor Fusion For Ground Robots, Ejup Hoxha

Dissertations and Theses

In underground, underwater and indoor environments, a robot has to rely solely on its on-board sensors to sense and understand its surroundings. This is the main reason why SLAM gained the popularity it has today. In recent years, we have seen excellent improvement on accuracy of localization using cameras and combinations of different sensors, especially camera-IMU (VIO) fusion. Incorporating more sensors leads to improvement of accuracy,but also robustness of SLAM. However, while testing SLAM in our ground robots, we have seen a decrease in performance quality when using the same algorithms on flying vehicles.We have an additional sensor for ground …

Elucidating The Properties And Mechanism For Cellulose Dissolution In Tetrabutylphosphonium-Based Ionic Liquids Using High Concentrations Of Water, Brad Crawford

Graduate Theses, Dissertations, and Problem Reports

The structural, transport, and thermodynamic properties related to cellulose dissolution by tetrabutylphosphonium chloride (TBPCl) and tetrabutylphosphonium hydroxide (TBPH)-water mixtures have been calculated via molecular dynamics simulations. For both ionic liquid (IL)-water solutions, water veins begin to form between the TBPs interlocking arms at 80 mol % water, opening a pathway for the diffusion of the anions, cations, and water. The water veins allow for a diffusion regime shift in the concentration region from 80 to 92.5 mol % water, providing a higher probability of solvent interaction with the dissolving cellulose strand. The hydrogen bonding was compared between small and large …

Statistical Inference For Networks Of High-Dimensional Point Processes, Xu Wang, Mladen Kolar, Ali Shojaie

UW Biostatistics Working Paper Series

Fueled in part by recent applications in neuroscience, high-dimensional Hawkes process have become a popular tool for modeling the network of interactions among multivariate point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work have only focused on estimation. To bridge this gap, this paper proposes a high-dimensional statistical inference procedure with theoretical guarantees for multivariate Hawkes process. Key to this inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarizes the entire history of the process. We apply this …

On The Sparre-Andersen Risk Models, Ruixi Zhang

Electronic Thesis and Dissertation Repository

This thesis develops several strategies for calculating ruin-related quantities for a variety of extended risk models. We focus on the Sparre-Andersen risk model, also known as the renewal risk model. The idea of arbitrary distribution for the waiting time between claim payments arose in the 1950’s from the collective risk theory, and received many extensions and modifications in recent years. Our goal is to tackle model assumptions that are either too relaxed for traditional methods to apply, or so complicated that elaborate algebraic tools are needed to obtain explicit solutions.

In Chapter 2, we consider a Lévy risk process and …

Characterization Of The Anomalous Ph Of Aqueous Nanoemulsions, Kieran P. Ramos

Doctoral Dissertations

Aqueous water-in-oil nanoemulsions have emerged as a versatile tool for use in microfluidics, drug delivery, single-molecule measurements, and other research. Nanoemulsions are often prepared with perfluorocarbons which are remarkably biocompatbile due to their stability, low surface tension, lipophobicity, and hydrophobicity. Therefore it is often assumed that droplet contents are unperturbed by the perfluorinated surface. However, in microemulsions, which are similar to nanoemulsions, it is known that either the pH of the aqueous phase or the ionization constants of encapsulated molecules are different from bulk solution. There is also recent evidence of low pH in perfluorinated aqueous nanoemulsions. The current underlying …

Function And Dissipation In Finite State Automata - From Computing To Intelligence And Back, Natesh Ganesh

Doctoral Dissertations

Society has benefited from the technological revolution and the tremendous growth in computing powered by Moore's law. However, we are fast approaching the ultimate physical limits in terms of both device sizes and the associated energy dissipation. It is important to characterize these limits in a physically grounded and implementation-agnostic manner, in order to capture the fundamental energy dissipation costs associated with performing computing operations with classical information in nano-scale quantum systems. It is also necessary to identify and understand the effect of quantum in-distinguishability, noise, and device variability on these dissipation limits. Identifying these parameters is crucial to designing …

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Probabilistic Models For Order-Picking Operations With Multiple In-The-Aisle Pick Positions, Jingming Liu

Graduate Theses and Dissertations

The development of probability density functions (pdfs) for travel time of a narrow aisle lift truck (NALT) and an automated storage and retrieval (AS/R) machine is the focus of the dissertation. The multiple in-the-aisle pick positions (MIAPP) order picking system can be modeled as an M/G/1 queueing problem in which storage and retrieval requests are the customers and the vehicle (NALT or AS/R machine) is the server. Service time is the sum of travel time and the deterministic time to pick up and deposit a pallet (TPD).

Our first contribution is the development of travel time pdfs for retrieval operations …

Some Recent Developments On Pareto-Optimal Reinsurance, Wenjun Jiang

Electronic Thesis and Dissertation Repository

This thesis focuses on developing Pareto-optimal reinsurance policy which considers the interests of both the insurer and the reinsurer. The optimal insurance/reinsurance design has been extensively studied in actuarial science literature, while in early years most studies were concentrated on optimizing the insurer’s interests. However, as early as 1960s, Borch argued that “an agreement which is quite attractive to one party may not be acceptable to its counterparty” and he pioneered the study on “fair” risk sharing between the insurer and the reinsurer. Quite recently, the question of how to strike a balance in risk sharing between an insurer and …

Using Random Forests To Estimate Win Probability Before Each Play Of An Nfl Game, Dennis Lock, Dan Nettleton

Dan Nettleton

Before any play of a National Football League (NFL) game, the probability that a given team will win depends on many situational variables (such as time remaining, yards to go for a first down, field position and current score) as well as the relative quality of the two teams as quantified by the Las Vegas point spread. We use a random forest method to combine pre-play variables to estimate Win Probability (WP) before any play of an NFL game. When a subset of NFL play-by-play data for the 12 seasons from 2001 to 2012 is used as a training dataset, …

Allocative Poisson Factorization For Computational Social Science, Aaron Schein

Doctoral Dissertations

Social science data often comes in the form of high-dimensional discrete data such as categorical survey responses, social interaction records, or text. These data sets exhibit high degrees of sparsity, missingness, overdispersion, and burstiness, all of which present challenges to traditional statistical modeling techniques. The framework of Poisson factorization (PF) has emerged in recent years as a natural way to model high-dimensional discrete data sets. This framework assumes that each observed count in a data set is a Poisson random variable $y ~ Pois(\mu)$ whose rate parameter $\mu$ is a function of shared model parameters. This thesis examines a specific …

The Martingale Approach To Financial Mathematics, Jordan M. Rowley

Master's Theses

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …

An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber

Electronic Theses and Dissertations

Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way …

A Statistical Analysis Of The Roulette Martingale System: Examples, Formulas And Simulations With R, Peter Pflaumer

International Conference on Gambling & Risk Taking

Some gamblers use a martingale or doubling strategy as a way of improving their chances of winning. This paper derives important formulas for the martingale strategy, such as the distribution, the expected value, the standard deviation of the profit, the risk of a loss or the expected bet of one or multiple martingale rounds. A computer simulation study with R of the doubling strategy is presented. The results of doubling to gambling with a constant sized bet on simple chances (red or black numbers, even or odd numbers, and low (1 – 18) or high (19 – 36) numbers) and …

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.