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 …

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 …

Establishing The Validity And Reliability Of The Locus Assessments, Tim Jacobbe, Bob Delmas, Brad Hartlaub, Jeff Haberstroh, Catherine Case, Steven Foti, Douglas Whitaker

Numeracy

The development of assessments as part of the funded LOCUS project is described. The assessments measure students’ conceptual understanding of statistics as outlined in the GAISE PreK–12 Framework. Results are reported from a large-scale administration to 3,430 students in grades 6 through 12 in the United States. Items were designed to assess levels of understanding as well as components of the statistical problem solving process as articulated in the GAISE framework. We discuss details of how the model used to develop the LOCUS assessments guided the gathering of evidence for validity and reliability arguments. Three types of validity evidence are …

Psychometric Properties Of A Combined Go/No-Go And Continuous Performance Task Across Childhood, Caron A.C. Clark, Kaitlyn Cook, Rui Wang, Michael Rueschman, Jerilynn Radcliffe, Susan Redline, H. Gerry Taylor

Statistical and Data Sciences: Faculty Publications

Despite the critical importance of attention for children’s self-regulation and mental health, there are few task-based measures of this construct appropriate for use across a wide childhood age range including very young children. Three versions of a combined go/no-go and continuous performance task (GNG/CPT) were created with varying length and timing parameters to maximize their appropriateness for age groups spanning early to middle childhood. As part of the baseline assessment of a clinical trial, 452 children aged 3–12 years (50% male, 50% female; 52% White, non-Hispanic, 27% Black, 16% Hispanic/Latinx; 6% other ethnicity/race) completed the task. Confirmatory factor analysis indicated …

Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", Jadon Wagstaff, Jesse Wheeler, Brennan Bean, Marc Maguire, Yan Sun

Browse all Datasets

Recent amendments to design ground snow load requirements in ASCE 7-22 have reduced the size of case study regions by 91% from what they were in ASCE 7-16, primarily in western states. This reduction is made possible through the development of highly accurate regional generalized additive regression models (RGAMs), stitched together with a novel smoothing scheme implemented in the R software package remap, to produce the continental- scale maps of reliability-targeted design ground snow loads available in ASCE 7-22. This approach allows for better characterizations of the changing relationship between temperature, elevation, and ground snow loads across the Conterminous United …

Inequalities For Interval-Valued Riemann Diamond-Alpha Integrals, Martin Bohner, Linh Nguyen, Baruch Schneider, Tri Truong

Mathematics and Statistics Faculty Research & Creative Works

We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond alpha Hölder's and Minkowski's interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.

Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We Shall Establish Some New Criteria for the Oscillation of Certain Second-Order Noncanonical Dynamic Equations with a Sublinear Neutral Term. This Task is Accomplished by Reducing the Involved Nonlinear Dynamic Equation to a Second-Order Linear Dynamic Inequality. We Also Establish Some New Oscillation Theorems Involving Certain Integral Conditions. Three Examples, Illustrating Our Results, Are Presented. Our Results Generalize Results for Corresponding Differential and Difference Equations.

Trilinear Immersed-Finite-Element Method For Three-Dimensional Anisotropic Interface Problems In Plasma Thrusters, Yajie Han, Guangqing Xia, Chang Lu, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

Accurately solving the anisotropic interface problem is one of the difficulties in aerospace plasma applications. Based on cubic Cartesian meshes, this paper develops a trilinear nonhomogeneous immersed finite element (IFE) method for solving the complex anisotropic 3D elliptic interface model with nonhomogeneous flux jump. Compared with the existing 3D linear IFE spaces based on tetrahedron meshes, the newly designed trilinear IFE space for the target model simplifies the mesh generation, significantly reduces the number of mesh elements and interface elements, provides much more convenient and efficient ways for finding the intersections between interfaces and mesh edges, and decreases the errors. …

Wright State University Fact Sheet, 2022-2023, Office Of Institutional Research & Effectiveness, Wright State University

Wright State University Fact Sheets

The Wright State University Fact Sheet showcasing numbers and statistics for Wright State University including demographics, funding, programs, and employment for the 2022-2023 academic year.

Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a …

Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a …

The Generalized Lyapunov Function As Ao’S Potential Function: Existence In Dimensions 1 And 2, Haoyu Wang, Wenqing Hu, Xiaoliang Gan, Ping Ao

Mathematics and Statistics Faculty Research & Creative Works

By using Ao's decomposition for stochastic dynamical systems, a new notion of potential function has been introduced by Ao and his collabora-tors recently. We show that this potential function agrees with the generalized Lyapunov function of the deterministic part of the stochastic dynamical sys-tem. We further prove the existence of Ao's potential function in dimensions 1 and 2 via the solution theory of first-order partial differential equations. Our framework reveals the equivalence between Ao's potential function and Lyapunov function, the latter being one of the most significant central notions in dynamical systems. Using this equivalence, our existence proof can also …

Three Solutions For Discrete Anisotropic Kirchhoff-Type Problems, Martin Bohner, Giuseppe Caristi, Ahmad Ghobadi, Shapour Heidarkhani

Mathematics and Statistics Faculty Research & Creative Works

In this article, using critical point theory and variational methods, we investigate the existence of at least three solutions for a class of double eigenvalue discrete anisotropic Kirchhoff-type problems. An example is presented to demonstrate the applicability of our main theoretical findings.