Probability Commons^™

Application Of Probabilistic Ranking Systems On Women’S Junior Division Beach Volleyball, Cameron Stewart, Michael Mazel, Bivin Sadler

SMU Data Science Review

Women’s beach volleyball is one of the fastest growing collegiate sports today. The increase in popularity has come with an increase in valuable scholarship opportunities across the country. With thousands of athletes to sort through, college scouts depend on websites that aggregate tournament results and rank players nationally. This project partnered with the company Volleyball Life, who is the current market leader in the ranking space of junior beach volleyball players. Utilizing the tournament information provided by Volleyball Life, this study explored replacements to the current ranking systems, which are designed to aggregate player points from recent tournament placements ...

Random Walks In The Quarter Plane: Solvable Models With An Analytical Approach, Harshita Bali, Enrico Au-Yeung

DePaul Discoveries

Initially, an urn contains 3 blue balls and 1 red ball. A ball is randomly chosen from the urn. The ball is returned to the urn, together with one additional ball of the same type (red or blue). When the urn has twenty balls in it, what is the probability that exactly ten balls are blue? This is a model for a random process. This urn model has been extended in various ways and we consider some of these generalizations. Urn models can be formulated as random walks in the quarter plane. Our findings indicate that for a specific type ...

New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie

Electronic Thesis and Dissertation Repository

This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.

The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In ...

Rewriting The Rules For Diagnostics: Implications Of Probability And Measure Theory For Sars-Cov-2 Testing, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

All Dissertations

Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to ...

Some Improved Markov Chain Convergence Rates, Fun Choi John Chan

All Dissertations

Explicit convergence rates to equilibrium are established for non reversible Markov chains not having an atom via coupling methods. We consider two Markov chains having the same transition function but different initial conditions on the same probability space, that is, a coupling. A random time is constructed so that subsequent to the random time the two processes are identical. Exploiting a shadowing condition, we show that it is possible to bound the tail distribution of the random time using only one of the chains. This bound gives the convergence rate to equilibrium for the Markov chain. The method is then ...

Anticipating Stochastic Integrals And Related Linear Stochastic Differential Equations, Sudip Sinha

LSU Doctoral Dissertations

Itô’s stochastic calculus revolutionized the field of stochastic analysis and has found numerous applications in a wide variety of disciplines. Itô’s theory, even though quite general, cannot handle anticipating stochastic processes as integrands. There have been considerable efforts within the mathematical community to extend Itô’s calculus to account for anticipation. The Ayed–Kuo integral — introduced in 2008 — is one of the most recent developments. It is arguably the most accessible among the theories extending Itô’s calculus — relying solely on probabilistic methods. In this dissertation, we look at the recent advances in this area, highlighting our contributions ...

General Stochastic Calculus And Applications, Pujan Shrestha

LSU Doctoral Dissertations

In 1942, K. Itô published his pioneering paper on stochastic integration with respect to Brownian motion. This work led to the framework for Itô calculus. Note that, Itô calculus is limited in working with knowledge from the future. There have been many generalizations of the stochastic integral in being able to do so. In 2008, W. Ayed and H.-H. Kuo introduced a new stochastic integral by splitting the integrand into the adaptive part and the counterpart called instantly independent. In this doctoral work, we conduct deeper research into the Ayed–Kuo stochastic integral and corresponding anticipating stochastic calculus.

We ...

Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano

Electrical and Computer Engineering ETDs

Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect ...

On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev

Mathematical and Statistical Sciences Faculty Publications and Presentations

The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We study a situation when the rate parameters of the exponential variables are not all different from each other. We obtain a representation for the Laplace transform of the hypoexponential distribution in the case of two repeated parameter values. Applying this decomposition, we prove a characterization of the exponential distribution.

Session 5: Equipment Finance Credit Risk Modeling - A Case Study In Creative Model Development & Nimble Data Engineering, Edward Krueger, Landon Thompson, Josh Moore

SDSU Data Science Symposium

This presentation will focus first on providing an overview of Channel and the Risk Analytics team that performed this case study. Given that context, we’ll then dive into our approach for building the modeling development data set, techniques and tools used to develop and implement the model into a production environment, and some of the challenges faced upon launch. Then, the presentation will pivot to the data engineering pipeline. During this portion, we will explore the application process and what happens to the data we collect. This will include how we extract & store the data along with how it ...

Mathematically Modeling Prey-Catching Behavior Of The Tomato Frog, Conrad Tyler, Sarah Marzen, Jenna Monroy

Spora: A Journal of Biomathematics

Many microhylid frog species, such as the tomato frog, Dyscophus sp., have demonstrated the ability to aim their tongues independently of head and jaw movements. However, a trade-off between tongue-aiming and head-only aiming exists in which the former allows for crypsis but lacks speed whereas the latter is faster but less accurate and more noticeable to prey. For frogs that can move their tongues independently of their heads, under what circumstances will they utilize each strategy, and why? We derive a model, dependent on factors relevant for prey-catching, for the probability the frog will turn its head (and not tongue ...

Analysis Of Minor League Rule Changes Effect On Stolen Bases, Zachary Houghtaling

Williams Honors College, Honors Research Projects

This study uses various statistical analyses to evaluate the justification of rule changes for Major League Baseball that were implemented within the Minor Leagues during the 2021 minor league season. The primary focus of the study is predicting how some of these Minor League rule changes could affect the stolen base success rate and the number of attempts per game within the Major Leagues. A survey was conducted to evaluate how fans feel about stolen bases within the current game and if rules should be altered to increase the number of stolen bases that occur. Additionally, recorded Major and Minor ...

Searching For Anomalous Extensive Air Showers Using The Pierre Auger Observatory Fluorescence Detector, Andrew Puyleart

Dissertations, Master's Theses and Master's Reports

Anomalous extensive air showers have yet to be detected by cosmic ray observatories. Fluorescence detectors provide a way to view the air showers created by cosmic rays with primary energies reaching up to hundreds of EeV . The resulting air showers produced by these highly energetic collisions can contain features that deviate from average air showers. Detection of these anomalous events may provide information into unknown regions of particle physics, and place constraints on cross-sectional interaction lengths of protons. In this dissertation, I propose measurements of extensive air shower profiles that are used in a machine learning pipeline to distinguish a ...

Lake Huron Shoreline Analysis, Shubham Satish Nandanwar

Theses and Dissertations (Comprehensive)

Lake Huron is a popular tourist destination and is home to several businesses and residents. Since the shoreline is dynamic and is subject to change over the years due to several factors such as a change in water level, soil type, human encroachment, etc., these locations tend to encounter floods due to increased water levels and wind speed. This causes erosion and loss to the properties along the shoreline.

This study is based on two areas of interest named Pinery Provincial Park and Sauble Beach which are located on the shoreline of Lake Huron where Pinery Provincial Park is a ...

Identification And Characterization Of Forest Fire Risk Zones Leveraging Machine Learning Methods, Joshua Balson, Matt Chinchilla, Cam Lu, Jeff Washburn, Nibhrat Lohia

SMU Data Science Review

Across the United States, record numbers of wildfires are observed costing billions of dollars in property damage, polluting the environment, and putting lives at risk. The ability of emergency management professionals, city planners, and private entities such as insurance companies to determine if an area is at higher risk of a fire breaking out has never been greater. This paper proposes a novel methodology for identifying and characterizing zones with increased risks of forest fires. Methods involving machine learning techniques use the widely available and recorded data, thus making it possible to implement the tool quickly.

(R1239) A New Type Ii Half Logistic-G Family Of Distributions With Properties, Regression Models, System Reliability And Applications, Emrah Altun, Morad Alizadeh, Haitham M. Yousof, Mahdi Rasekhi, G. G. Hamedani

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a new family of distributions based on the half logistic distribution. With the new family, the baseline distributions gain flexibility through additional shape parameters. The important statistical properties of the proposed family are derived. A new generalization of the Weibull distribution is used to introduce a location-scale regression model for the censored response variable. The utility of the introduced models is demonstrated in survival analysis and estimation of the system reliability. Three data sets are analyzed. According to the empirical results, it is observed that the proposed family gives better results than other existing models.

(R1887) Inferring Trends Of Point Processes From Non-Iid Samples, Bruno Appolloni

Applications and Applied Mathematics: An International Journal (AAM)

We discuss unprecedented, albeit rudimentary, tools to infer the evolution of a point process where the available samples are both truncated and non independently drawn. To achieve this goal, we lay in an intermediate domain between probability models and fuzzy sets, still maintaining probabilistic features of the employed statistics as the reference KPI of the tools. The overall strategy is to frame the problem within the Algorithmic Inference framework and use a sort of kernel trick to distort the seeds of the observed variable so as to render them an iid sample of a random variable in a proper feature ...

(R1505) A Note On Large Deviations In Insurance Risk, Stefan Gerhold

Applications and Applied Mathematics: An International Journal (AAM)

We study large and moderate deviations for an insurance portfolio, with the number of claims tending to infinity, without assuming identically distributed claims. The crucial assumption is that the centered claims are bounded, and that variances are bounded below. From a general large deviations upper bound, we obtain an exponential bound for the probability of the average loss exceeding a threshold. A counterexample shows that a full large deviation principle, including also a lower bound, does not follow from our assumptions. We argue that our assumptions make sense, in particular, for life insurance portfolios and discuss how to apply our ...