Statistics and Probability Commons^™

Stochastic Modeling Of Earthquakes And Option Pricing Using Bns-Gamma-Ou Model, Mandela Bright Quashie

Open Access Theses & Dissertations

High frequency data are becoming increasingly popular these days. They are fundamental in basically every facet of people’s lives. They are the determining factors in hedging in the field of finance. In geology, they help in the accurate prediction of earthquakes’ magnitude which goes along way to help save lives and properties.

High frequency data are also used more and more frequently for speculations. For this reason, it is important not only for scientists to apply models allowing correct quantification of these data, but also to improve the eciency of these models.

The Black-Scholes model, which is widely used because …

Technological Software In Mathematics, Courtney Kish

Williams Honors College, Honors Research Projects

Technology has been advancing significantly over the years. One area that has been affected is mathematics. Technological software has been developed that has allowed for mathematics to be done using software programs. For example, WebAssign allows students to complete online math homework and example practice problems, as well as watch videos to explain topics in math. However, like all things, this is not without downfalls. While this technology offers students access to online lectures and instant feedback, cheating and costly expenses also come with it.

In this research paper, I will discuss the benefits and shortcomings of different technological software …

Home Sales As A Time Series Model, Noah R. Hellenthal

Williams Honors College, Honors Research Projects

Rational Expectations Hypothesis is an economic theorem that states that our best way to predict the future is by looking at the past. While this theory is typically used to address inflation, the same concept can be used when predicting future home sales. With the failure of subprime mortgages and the burst of the housing market bubble in 2008, home sales are proven to be an appropriate indication of how the U.S. economy is performing. Through time series analysis, I will be able to construct a model with monthly home sales data from the U.S. Census Bureau. Due to seasonality …

Spatially Adaptive Estimation Of Spectrum, Yi None Xie

Open Access Theses & Dissertations

When analyzing a stationary time series, one of the questions we are often interested in is how to estimate its spectrum. Many approaches have been proposed to this end. Most are focused on smoothing the periodogram using a single smoothing parameter across all Fourier frequencies. In this paper, we smooth the log periodogram by placing a spatially adaptive prior called the dynamic shrinkage prior, so that varying degrees of smoothing may be applied to different intervals of Fourier frequencies, resulting in less biased estimates of the spectrum. Further research will extend this approach to spectral estimation for nonstationary time series.

An Examination Of Covid-19 Statistical Modeling, Shane Vaughan

Williams Honors College, Honors Research Projects

The 2019 novel coronavirus, also known as COVID-19, is an infectious disease which was first reported in late 2019 and soon spread to become a global pandemic, prompting major action from world governments. Soon after, many institutions began attempts to analyze and predict the spread and severity of the disease via statistical modeling. Some information is not available for public consumption; however, a number of institutions have published the results of their analyses and some have made public repositories of the code used to build the models. This research paper attempts use these and other resources to examine the modeling …

Ai And Machine Learning Usage In Actuarial Science, Joanna Riley

Williams Honors College, Honors Research Projects

Some people in the world work hard and do whatever it takes in order to get a job that they love. There are others that don’t care about their jobs and solely perform them in order to make money. So, there are individuals or groups that wouldn’t care if a machine or computer were to replace them in their job, but others would be devastated. The question for this paper is: Can actuaries be completely replaced by computers, or do we need the human mind in order to make proper decisions and judgements?

Key words and phrases: actuarial science, artificial …

Generalization Of Kullback-Leibler Divergence For Multi-Stage Diseases: Application To Diagnostic Test Accuracy And Optimal Cut-Points Selection Criterion, Chen Mo

College of Graduate Studies: Theses & Dissertations

The Kullback-Leibler divergence (KL), which captures the disparity between two distributions, has been considered as a measure for determining the diagnostic performance of an ordinal diagnostic test. This study applies KL and further generalizes it to comprehensively measure the diagnostic accuracy test for multi-stage (K > 2) diseases, named generalized total Kullback-Leibler divergence (GTKL). Also, GTKL is proposed as an optimal cut-points selection criterion for discriminating subjects among different disease stages. Moreover, the study investigates a variety of applications of GTKL on measuring the rule-in/out potentials in the single-stage and multi-stage levels. Intensive simulation studies are conducted to compare the performance …

Accounting For The Uncertainty Due To Chemicals Below The Detection Limit In Mixture Analysis, Paul M. Hargarten

Theses and Dissertations

Humans are exposed to multiple chemicals every day. Epidemiological studies have shown that chemical mixtures are associated with cancers, allergies, neurodevelopmental disorders, and other adverse health effects. To assess these associations, investigators are increasingly using chemical mixture approaches like weighted quantile sum (WQS) regression. In these studies, the research objectives are to determine whether a mixture of correlated chemicals is associated with an adverse health outcome and to identify the important chemicals. However, as experimental equipment measures each exposure to a chemical-specific detection limit, the exposures are unknown between zero and the detection limit. Indeed, the number of exposures below …

The Effect Of Time And Temperature On The Quality Of Latent Fingerprints On Incandescent Lightbulbs, Varying Donors Age And Sex, Kinaysha M. Collazo Maldonado

Master of Science in Forensic Science Directed Research Projects

Fingerprints are used as a means of identification, but there are no established methodologies to determine time since deposition of latent fingerprints by visual means alone. This research considered the influence of age and sex on the quality of recovered latent prints from lit and unlit lightbulbs from 1 to 10 days, using accumulated degree hours (ADH) to account for both heat and time simultaneously. Two male and two female donors (one of each aged40 years) were used. A thermal imaging camera was used to monitor the lightbulbs top and middle regions, which were significantly different (p≤0.05) for the experimental …

The Role Of Topography, Soil, And Remotely Sensed Vegetation Condition Towards Predicting Crop Yield, Trenton E. Franz, Sayli Pokal, Justin P. Gibson, Yuzhen Zhou, Hamed Gholizadeh, Fatima Amor Tenorio, Daran Rudnick, Derek M. Heeren, Matthew F. Mccabe, Matteo Ziliani, Zhenong Jin, Kaiyu Guan, Ming Pan, John Gates, Brian Wardlow

School of Natural Resources: Faculty Publications

Foreknowledge of the spatiotemporal drivers of crop yield would provide a valuable source of information to optimize on-farm inputs and maximize profitability. In recent years, an abundance of spatial data providing information on soils, topography, and vegetation condition have become available from both proximal and remote sensing platforms. Given the wide range of data costs (between USD $0−50/ha), it is important to understand where often limited financial resources should be directed to optimize field production. Two key questions arise. First, will these data actually aid in better fine-resolution yield prediction to help optimize crop management and farm economics? Second, what …

Distribution Of Human Exposure To Ozone During Commuting Hours In Connecticut Using The Cellular Device Network, Owais Gilani, Simon Urbanek, Michael J. Kane

Faculty Journal Articles

Epidemiologic studies have established associations between various air pollutants and adverse health outcomes for adults and children. Due to high costs of monitoring air pollutant concentrations for subjects enrolled in a study, statisticians predict exposure concentrations from spatial models that are developed using concentrations monitored at a few sites. In the absence of detailed information on when and where subjects move during the study window, researchers typically assume that the subjects spend their entire day at home, school, or work. This assumption can potentially lead to large exposure assignment bias. In this study, we aim to determine the distribution of …

Tropical Cyclone Hazards In Relation To Propagation Speed, Jiehao Huang

Dissertations and Theses

As the population and infrastructure along the US East Coast increase, it becomes increasingly important to study the characteristics of tropical cyclones that can impact the coast. A recent study shows that the propagation speed of tropical cyclones has slowed over the past 60 years, which can lead to greater accumulation of precipitation and greater storm surge impacts. The study presented herein is meant to examine and analyze the relationships that exist between the propagation speed of tropical cyclones, their surface wind strength, displacement angles, and cyclone averaged winds. This analysis is focused on tropical cyclones spanning from 1950-2015 in …

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 …

K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin

CMC Senior Theses

The 2015 article Creating Diversified Portfolios Using Cluster Analysis proposes an algorithm that uses the Sharpe ratio and results from K-means clustering conducted on companies' historical financial ratios to generate stock market portfolios. This project seeks to evaluate the performance of the portfolio-building algorithm during the beginning period of the COVID-19 recession. S&P 500 companies' historical stock price movement and their historical return on assets and asset turnover ratios are used as dissimilarity metrics for K-means clustering. After clustering, stock with the highest Sharpe ratio from each cluster is picked to become a part of the portfolio. The economic and …

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 …

Predictors Of Colorectal Cancer Screening Among Maryland Adults, Aged 50–75 Years, Pamela Manwi Asangong

Walden Dissertations and Doctoral Studies

Screening plays an essential role in reducing colorectal cancer (CRC) incidence and mortality rates, yet CRC screening use remains low in Maryland and lower in some age and racial/ethnic groups with limited resources to participate in CRC screening programs. The purpose of this quantitative, cross-sectional study is to investigate whether age group, sex, race/ethnicity, education level, income level, health insurance coverage, and access to health care professional can predict an individual, 50–75 years of age, in Maryland to take action to fully meet the United States Preventive Services Task Force CRC screening test recommendation within the recommended time interval. The …

Comparative Survival Of Asian And White Metastatic Castration-Resistant Prostate Cancer Men Treated With Docetaxel, Susan Halabi, Sandipan Dutta, Catherine M. Tangen, Mark Rosenthal, Daniel P. Petrylak, Ian M. Thompson Jr., Kim N. Chi, Johann S. De Bono, John C. Araujo, Christopher Logothetis, Mario A. Eisenberger, David I. Quinn, Karim Fizazi, Michael J. Morris, Celestia S. Higano, Ian F. Tannock, Eric J. Small, William Kevin Kelly

Mathematics & Statistics Faculty Publications

There are few data regarding disparities in overall survival (OS) between Asian and white men with metastatic castration-resistant prostate cancer (mCRPC). We compared OS of Asian and white mCRPC men treated in phase III clinical trials with docetaxel and prednisone (DP) or a DP-containing regimen. Individual participant data from 8820 men with mCRPC randomly assigned on nine phase III trials to receive DP or a DP-containing regimen were combined. Men enrolled in these trials had a diagnosis of prostate adenocarcinoma. The median overall survival was 18.8 months (95% confidence interval [CI] = 17.4 to 22.1 months) and 21.2 months (95% …

Cosmic: Us-Based Conversion Master's Degree In Computing, Gary S. Krenz, Thomas Kaczmarek

Mathematical and Statistical Science Faculty Research and Publications

COSMIC is an NSF S-STEM graduate curriculum initiative/conversion program that strives to provide an accelerated pathway to a Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over into the computing field. The structure of our conversion program, the context that motivated it, and insights from conversion students' instructors are presented. Program successes with students from under-represented populations and the limitations that are also experienced are discussed. Our conversion program is based on a highly focused summer bridge course, combined with a customized curriculum pathway that enables people …

Evaluating The Accuracy Of Firearm Examiner Conclusions Using Cartridge Case Reproductions, Eric Freeman Law

Graduate Theses, Dissertations, and Problem Reports (ETD)

The forensic science pattern comparison areas, including fingerprints, footwear, and firearms, have been criticized for their subjective nature. While much research has attempted to move these disciplines to more objective methods, a majority of examiners are still coming to conclusions based on their own training and experience. To compare accuracy between examiners, a method called double-casting was used in this study to create plastic cartridge case reproductions. In the first part of this study, double-cast accuracy was evaluated using two automated comparison systems to quantify the similarity. It was determined that the double-casting method used here produces accurate reproductions with …

Modeling The Galactic Compact Binary Neutron Star Population And Studying The Double Pulsar System, Nihan Pol

Graduate Theses, Dissertations, and Problem Reports (ETD)

Binary neutron star (BNS) systems consisting of at least one neutron star provide an avenue for testing a broad range of physical phenomena ranging from tests of General Relativity to probing magnetospheric physics to understanding the behavior of matter in the densest environments in the Universe. Ultra-compact BNS systems with orbital periods less than few tens of minutes emit gravitational waves with frequencies ~mHz and are detectable by the planned space-based Laser Interferometer Space Antenna (LISA), while merging BNS systems produce a chirping gravitational wave signal that can be detected by the ground-based Laser Interferometer Gravitational-Wave Observatory (LIGO). Thus, BNS …

Three Essays On Health Economics And Policy Evaluation, Shishir Shakya

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation consists of three essays on the U.S. Health care policy. Each paragraph below refers to the three abstracts for the three chapters in this dissertation, respectively. I provide quantitative evidence on how much Prescription Drug Monitoring Programs (PDMPs) affects the retail opioid prescribing behaviors. Using the American Community Survey (ACS), I retrieve county-level high dimensional panel data set from 2010 to 2017. I employ three separate identification strategies: difference-in-difference, double selection post-LASSO, and spatial difference-in-difference. I compare how the retail opioid prescribing behaviors of counties, that are mandatory for prescribers to check the PDMP before prescribing controlled substances …

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

Graduate Theses, Dissertations, and Problem Reports (ETD)

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 …

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 (ETD)

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 …

Process Based Analysis Of Fluvial Stratigraphic Record: Middle Pennsylvanian Allegheny Formation, North-Central Wv, Oluwasegun O. Abatan

Graduate Theses, Dissertations, and Problem Reports (ETD)

Fluvial deposits represent some of the best hydrocarbon reservoirs, but the quality of fluvial reservoirs varies depending on the reservoir architecture, which is controlled by allogenic and autogenic processes. Allogenic controls, including paleoclimate, tectonics, and glacio-eustasy, have long been debated as dominant controls in the deposition of fluvial strata. However, recent research has questioned the validity of this cyclicity and may indicate major influence from autogenic controls. To further investigate allogenic controls on stratal order, I analyzed the facies architecture, geomorphology, paleohydrology, and the stratigraphic framework of the Middle Pennsylvanian Allegheny Formation (MPAF), a fluvial depositional system in the Appalachian …

Interpretations Of Bicoherence In Space & Lab Plasma Dynamics, Gregory Allen Riggs

Graduate Theses, Dissertations, and Problem Reports (ETD)

The application of bicoherence analysis to plasma research, particularly in non-linear, coupled-wave regimes, has thus far been significantly belied by poor resolution in time, and/or outright destruction of frequency information. Though the typical power spectrum cloaks the phase-coherency between frequencies, Fourier transforms of higher-order convolutions provide an n-dimensional spectrum which is adept at elucidating n-wave phase coherence. As such, this investigation focuses on the utility of the normalized bispectrum for detection of wave-wave coupling in general, with emphasis on distinct implications within the scope of non-linear plasma physics. Interpretations of bicoherent features are given for time series from …

Inventory Models For Perishable Items Under Markdown Policy, Nurzahara Atika Kamaruzaman

Student Works (2020-2029)

As expected, the demand for a fresh product depends on how fresh it is, therefore, it is important to take expiration date into consideration. Based on marketing and economic theory, several factors such as price, inventory level and advertisement play a crucial role in influencing the demand. Hence, we study the effect of these factors in influencing the demand in the inventory model. Since the demand for perishable product declines over time, markdown policy is offered to increase the demand and profit while reducing the inventory. Salvage value is incorporated to the deteriorating units. In this research, we extend previous …

Mass Grave Localization Prediction With Geographical Information Systems In Guatemala And Future Impacts, Perla Santillan

Master of Science in Forensic Science Directed Research Projects

Conducting physical searches for mass grave locations based on anecdotal evidence is a time consuming and resource intensive endeavor in circumstances that often pose a threat to personal safety. The development of tools and procedures to speed such searches can greatly reduce the risk involved, increase the number of individuals whose remains are recovered and identified; and, more importantly, reunite these remains with their loved ones to provide them with a proper burial. Geographic information systems (GIS) software, which can analyze and manipulate the spatial characteristics of known mass grave data, represents a powerful tool that can be used to …

Bayesian Approach To Finding The Most Likely Circuit Structure, Shannon Harms

Graduate Research Theses & Dissertations

Systems, and their reliabilities, depend on the reliabilities of the components that theyare composed of, and in this paper we want to nd the system structure that is the most likely given observed data. Bayesian methods were utilized in order to discover the posterior means, or observed reliabilities, of both the components and the systems. Assuming the serial and parallel system structures have independent components, we calculated system reliabilities based on observed component reliabilities by using the multiplication and addi- tion probability rules. We are then able to expand upon the numerical comparison method through a maximum likelihood analysis that …

Construction Of Confidence Intervals For Parameter Estimates Of T-Distribution, Margaret Remus

Graduate Research Theses & Dissertations

Constructing confidence intervals is a standard statistical practice to estimate parameters of a distribution. Estimation of the parameters of a t-distribution can be computationally intensive. As a result, there are not clear defined formulas for the construction of confidence intervals for those estimates. Using the Normal confidence interval equation does not offer an accurate interval. Therefore, this paper will outline potential alternative methods for building confidence intervals to estimate the mean of a t-distribution. This paper will offer several methods and simulations to determine which method is best for constructing confidence intervals for varying sample sizes and degrees of freedom. …

Polarization In Social Networks Under A Proposed Model, Ashley L. Seyfried

Graduate Research Theses & Dissertations

The mathematical study of opinion dynamics started in 1956, with French. Since the explosion of social media, this study has increased in popularity. In this paper, we propose a new model to apply to a social network graph. With this model, the opinions of actors are in the range [0,1]. We use the Normal probability distribution to model these opinions in conjunction with a group of parameters. We allow for the uncertainty of members in the network. We then ran simulations to find the values of these parameters that do not lead to a network becoming polarized. Different states of …