Statistics and Probability Commons^™

A New Global Divergence Free And Pressure-Robust Hdg Method For Tangential Boundary Control Of Stokes Equations, Gang Chen, Wei Gong, Mariano Mateos, John R. Singler, Yangwen Zhang

Mathematics and Statistics Faculty Research & Creative Works

In Gong et al. (2020), we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optimal convergence rate for the optimal control that reflects its global regularity. However, the error estimates depend on the pressure, and the velocity is not divergence free. The importance of pressure-robust numerical methods for fluids was addressed by John et al. (2017). In this work, we devise a new HDG method to approximate the solution of the Stokes tangential boundary control problem; the HDG method is also of independent interest for solving the …

A New Global Divergence Free And Pressure-Robust Hdg Method For Tangential Boundary Control Of Stokes Equations, Gang Chen, Wei Gong, Mariano Mateos, John R. Singler, Yangwen Zhang

Mathematics and Statistics Faculty Research & Creative Works

In Gong et al. (2020), we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optimal convergence rate for the optimal control that reflects its global regularity. However, the error estimates depend on the pressure, and the velocity is not divergence free. The importance of pressure-robust numerical methods for fluids was addressed by John et al. (2017). In this work, we devise a new HDG method to approximate the solution of the Stokes tangential boundary control problem; the HDG method is also of independent interest for solving the …

Multicollinearity Applied Stepwise Stochastic Imputation: A Large Dataset Imputation Through Correlation‑Based Regression, Benjamin D. Leiby, Darryl K. Ahner

Faculty Publications

This paper presents a stochastic imputation approach for large datasets using a correlation selection methodology when preferred commercial packages struggle to iterate due to numerical problems. A variable range-based guard rail modification is proposed that benefits the convergence rate of data elements while simultaneously providing increased confidence in the plausibility of the imputations. A large country conflict dataset motivates the search to impute missing values well over a common threshold of 20% missingness. The Multicollinearity Applied Stepwise Stochastic imputation methodology (MASS-impute) capitalizes on correlation between variables within the dataset and uses model residuals to estimate unknown values. Examination of the …

The Probability Of Miracles, Lewis A. Pummell

CAFE Symposium 2023

An insight into the probability that we will experience a miracle within our lives. This project considers different ways of defining a miracle, and how this impacts how we consider them in our lives. They are paradoxical, and completely subjective - although there are key concepts of probability which will guide opinion.

The Use Of Probability In Quantum Mechanics To Calculate Measurement Outcomes, Hannah E. Collins

CAFE Symposium 2023

The concept of probability can help measure some of the possible outcomes of different experiments in the field of quantum mechanics. Those experiments include Thomas Young's double slit experiment, the Schrödinger equation, the wave function, and the Born Rule, which all make use of probability to predict the placement of certain subatomic particles including photons of light, in the experiments. In this project, the manner in which probability does this is explored in depth.

Looking For Life, Conor C. Grubb

CAFE Symposium 2023

The topic of aliens is not just about conspiracy theories and tinfoil hats, through the years numerous respected scientists have weighed in and put thought into the topic. The Search for Extraterrestrial Intelligence (SETI) is closely tied to the Fermi Paradox and the Drake Equation. The Fermi Paradox considers why humans haven't already interacted with aliens if they exist, and the Drake Equation outlines potential variables that would influence the chances of humanity receiving radio contact from an alien civilization.

Finite Mixture Modeling For Hierarchically Structured Data With Application To Keystroke Dynamics, Andrew Simpson, Semhar Michael

SDSU Data Science Symposium

Keystroke dynamics has been used to both authenticate users of computer systems and detect unauthorized users who attempt to access the system. Monitoring keystroke dynamics adds another level to computer security as passwords are often compromised. Keystrokes can also be continuously monitored long after a password has been entered and the user is accessing the system for added security. Many of the current methods that have been proposed are supervised methods in that they assume that the true user of each keystroke is known apriori. This is not always true for example with businesses and government agencies which have internal …

Two-Stage Approach For Forensic Handwriting Analysis, Ashlan J. Simpson, Danica M. Ommen

SDSU Data Science Symposium

Trained experts currently perform the handwriting analysis required in the criminal justice field, but this can create biases, delays, and expenses, leaving room for improvement. Prior research has sought to address this by analyzing handwriting through feature-based and score-based likelihood ratios for assessing evidence within a probabilistic framework. However, error rates are not well defined within this framework, making it difficult to evaluate the method and can lead to making a greater-than-expected number of errors when applying the approach. This research explores a method for assessing handwriting within the Two-Stage framework, which allows for quantifying error rates as recommended by …

Application Of Gaussian Mixture Models To Simulated Additive Manufacturing, Jason Hasse, Semhar Michael, Anamika Prasad

SDSU Data Science Symposium

Additive manufacturing (AM) is the process of building components through an iterative process of adding material in specific designs. AM has a wide range of process parameters that influence the quality of the component. This work applies Gaussian mixture models to detect clusters of similar stress values within and across components manufactured with varying process parameters. Further, a mixture of regression models is considered to simultaneously find groups and also fit regression within each group. The results are compared with a previous naive approach.

Models For Predicting Maximum Potential Intensity Of Tropical Cyclones, Iftekhar Chowdhury, Gemechis Djira

SDSU Data Science Symposium

Tropical cyclones (TCs) are considered as extreme weather events, which has a low-pressure center, namely an eye, strong winds, and a spiral arrangement of thunderstorms that produces heavy rain, storm surges, and can cause severe destruction in coastal areas worldwide. Therefore, reliable forecasts of the maximum potential intensity (MPI) of TCs are critical to estimate the damages to properties, lives, and risk assessment. In this study, we explore and propose various regression models, to predict the potential intensity of TCs in the North Atlantic at 12, 24, 36, 48, 60, and 72- hour forecasting lead time. In addition, a popular …

A Characterization Of Bias Introduced Into Forensic Source Identification When There Is A Subpopulation Structure In The Relevant Source Population., Dylan Borchert, Semhar Michael, Christopher Saunders

SDSU Data Science Symposium

In forensic source identification the forensic expert is responsible for providing a summary of the evidence that allows for a decision maker to make a logical and coherent decision concerning the source of some trace evidence of interest. The academic consensus is usually that this summary should take the form of a likelihood ratio (LR) that summarizes the likelihood of the trace evidence arising under two competing propositions. These competing propositions are usually referred to as the prosecution’s proposition, that the specified source is the actual source of the trace evidence, and the defense’s proposition, that another source in a …

Session 8: Ensemble Of Score Likelihood Ratios For The Common Source Problem, Federico Veneri, Danica M. Ommen

SDSU Data Science Symposium

Machine learning-based Score Likelihood Ratios have been proposed as an alternative to traditional Likelihood Ratios and Bayes Factor to quantify the value of evidence when contrasting two opposing propositions.

Under the common source problem, the opposing proposition relates to the inferential problem of assessing whether two items come from the same source. Machine learning techniques can be used to construct a (dis)similarity score for complex data when developing a traditional model is infeasible, and density estimation is used to estimate the likelihood of the scores under both propositions.

In practice, the metric and its distribution are developed using pairwise comparisons …

Post-Quantum Hermite-Jensen-Mercer Inequalities, Martin Bohner, Hüseyin Budak, Hasan Kara

Mathematics and Statistics Faculty Research & Creative Works

The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals.

Modeling And Fitting Two-Way Tables Containing Outliers, David L. Farnsworth

Articles

A model is proposed for two-way tables of measurement data containing outliers. The two independent variables are categorical and error free. Neither missing values nor replication are present. The model consists of the sum of a customary additive part that can be fit using least squares and a part that is composed of outliers. Recommendations are made for methods for identifying cells containing outliers and for fitting the model. A graph of the observations is used to determine the outliers’ locations. For all cells containing an outlier, replacement values are determined simultaneously using a classical missing-data tool. The result is …

Unlocking Potential: The School-To-Prison Pipeline For Students With Disabilities, Navena F. Chaitoo

Dissertations, Theses, and Capstone Projects

This research uses quasi-experimental, matched sampling to examine the school-to-prison pipeline for students with disabilities using data from the National Longitudinal Study of Adolescent to Adult Health. This study presents novel insights into an at-risk group that has faced disproportionate rates of school discipline and incarceration. The study finds school suspension to be associated with future involvement in the criminal legal system and lower educational attainment. Disability was not found to mediate the relationship between suspension and future involvement in the criminal legal system or the relationship between suspension and academic outcomes. However, disability was found to be a statistically …

Analyzing Relationships With Machine Learning, Oscar Ko

Dissertations, Theses, and Capstone Projects

Procedurally, this project aims to take a dataset, analyze it, and offer insights to the audience in an easy-to-digest format. Conceptually, this project will seek to explore questions like: “Do couples that meet through online dating or dating apps have higher or lower quality relationships?”, “Can any features in this dataset help predict how a subject would rate their relationship quality?”, and “What other insights can I derive from using machine learning for exploratory analysis?” The intended audience for this project is anyone interested in romantic relationships or machine learning.

The dataset is from a Stanford University survey, “How Couples …

Biasing Estimator To Mitigate Multicollinearity In Linear Regression Model, Abdulrasheed Bello Badawaire, Issam Dawoud, Adewale Folaranmi Lukman, Victoria Laoye, Arowolo Olatunji

Al-Bahir

A new two-parameter estimator was developed to combat the threat of multicollinearity for the linear regression model. Some necessary and sufficient conditions for the dominance of the proposed estimator over ordinary least squares (OLS) estimator, ridge regression estimator, Liu estimator, KL estimator, and some two-parameter estimators are obtained in the matrix mean square error sense. Theory and simulation results show that, under some conditions, the proposed two-parameter estimator consistently dominates other estimators considered in this study. The real-life application result follows suit.

Data Science Transfer Pathways From Associate's To Bachelor's Programs, Benjamin S. Baumer, Nicholas J. Horton

Statistical and Data Sciences: Faculty Publications

A substantial fraction of students who complete their college education at a public university in the United States begin their journey at one of the 935 public 2-year colleges. While the number of 4-year colleges offering bachelor’s degrees in data science continues to increase, data science instruction at many 2-year colleges lags behind. A major impediment is the relative paucity of introductory data science courses that serve multiple student audiences and can easily transfer. In addition, the lack of predefined transfer pathways (or articulation agreements) for data science creates a growing disconnect that leaves students who want to study data …

A Statistical Analysis Of The Change In Age Distribution Of Spawning Hatchery Salmon, Rachel Macaulay, Emily Barrett, Grace Penunuri, Eli E. Goldwyn

Spora: A Journal of Biomathematics

Declines in salmon sizes have been reported primarily as a result of younger maturation rates. This change in age distribution poses serious threats to salmon-dependent peoples and ecological systems. We perform a statistical analysis to examine the change in age structure of spawning Alaskan chum salmon Oncorhynchus keta and Chinook salmon O. tshawytscha using 30 years of hatchery data. To highlight the impacts of this change, we investigate the average number of fry/smolt that each age of spawning chum/Chinook salmon produce. Our findings demonstrate an increase in younger hatchery salmon populations returning to spawn, and fewer amounts of fry produced …

Beyond Statistical Significance: A Holistic View Of What Makes A Research Finding "Important", Jane E. Miller

Numeracy

Students often believe that statistical significance is the only determinant of whether a quantitative result is “important.” In this paper, I review traditional null hypothesis statistical testing to identify what questions inferential statistics can and cannot answer, including statistical significance, effect size and direction, causality, generalizability, and changeability of the independent variable. I illustrate these issues with examples from an empirical study of the association between how much time teenagers spent playing video games and time spent reading. I describe how study design and context determine each of those aspects of “importance,” and close by summarizing how to provide a …