Physical Sciences and Mathematics Commons^™

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 …

Forecasting Remission Time Of A Treatment Method For Leukemia As An Application To Statistical Inference Approach, Mahmoud Mansour, Rashad El-Sagheer, Ahmed Galal Attia, Beha S. El-Desouky Prof.

Basic Science Engineering

In this paper, Weibull-Linear Exponential distribution (WLED) has been investigated whether being it is a well-fit distribution to a clinical real data. These data represent the duration of remission achieved by a certain drug used in the treatment of leukemia for a group of patients. The statistical inference approach is used to estimate the parameters of the WLED through the set of the fitted data. The estimated parameters are utilized to evaluate the survival and hazard functions and hence assessing the treatment method through forecasting the duration of remission times of patients. A two-sample prediction approach has been applied to …

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 …

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 …

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

Al-Bahir Journal for Engineering and Pure Sciences

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 …

Nearby Galaxies: Modelling Star Formation Histories And Contamination By Unresolved Background Galaxies, Hadi Papei

Electronic Thesis and Dissertation Repository

Galaxies are complex systems of stars, gas, dust, and dark matter which evolve over billions of years, and one of the main goals of astrophysics is to understand how these complex systems form and change. Measuring the star formation history of nearby galaxies, in which thousands of stars can be resolved individually, has provided us with a clear picture of their evolutionary history and the evolution of galaxies in general.

In this work, we have developed the first public Python package, SFHPy, to measure star formation histories of nearby galaxies using their colour-magnitude diagrams. In this algorithm, an observed colour-magnitude …

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 …

On Partially Observed Tensor Regression, Dinara Miftyakhetdinova

Major Papers

Tensor data is widely used in modern data science. The interest lies in identifying and characterizing the relationship between tensor datasets and external covariates. These datasets, though, are often incomplete. An efficient nonconvex alternating updating algorithm proposed by J. Zhou et al. in the paper "Partially Observed Dynamic Tensor Response Regression" provides a novel approach. The algorithm handles the problem of unobserved entries by solving an optimization problem of a loss function under the low-rankness, sparsity, and fusion constraints. This analysis aims to understand in detail the proposed algorithms and their theoretical proofs with, potentially, dropping some of the assumptions …

Uniformity Test Based On The Empirical Bernstein Distribution, Ran Sun

Major Papers

In this paper, we firstly review the origin of Bernstein polynomial and the various application of it. Then we review the importance of goodness-of-fit test, especially the uniformity test, and we examine lots of different test statistics proposed by far. After that we suggest two new statistics for testing the uniformity. These two statistics are based on Komogorov-Smirnov test type and Cramér-Von Mises test type, respectively. Also we embed Bernstein polynomial into those test type and take advantage of great approximation performance of this polynomial. Finally, we run a Monte-Carlo simulation to compare the performance of our statistics to those …

Optimal Speed Of A Machine In An Assembly Line Using The Continuous Time Markov Chain Rate Matrix, Chandi Darshani Rupasinghe

Major Papers

The optimal speed of a machine in an assembly line is determined using a Markov decision process type model. We develop the rate matrix that represents the inter-event time of a machine, either repair time or time to breakdown, as a function of speed. We consider the rate of time to breakdown with a variety of functions of speed. We find limiting probabilities and express profit in terms of these probabilities. We then find the optimal speed to maximize profit. Further, we assume an underlying function of speed and simulate data using R. From the simulated data, we estimate the …

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. …

On Bayesian Methods And Functional Registration Of Fmri, Xiaoxuan Wang

Major Papers

The application of functional magnetic resonance imaging (fMRI) has greatly improved our comprehension of the human brain and behaviour. However, after anatomical alignment, there remains large inter-individual variability in brain anatomy and functional localization, which is one of the obstacles to conducting group studies and performing group-level inference. This major paper addresses this problem by applying a new method (Bayesian Functional Registration) to decrease misalignment in functional brain systems between people by spatially transforming each subject’s functional data into a common reference map. The proposed approach allows us to assess differences in brain function across subjects. It also creates a …

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 …

Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang

Mathematics and Statistics Faculty Research & Creative Works

We Propose Two Unconditionally Stable, Linear Ensemble Algorithms with Pre-Computable Shared Coefficient Matrices Across Different Realizations for the Magnetohydrodynamics Equations. the Viscous Terms Are Treated by a Standard Perturbative Discretization. the Nonlinear Terms Are Discretized Fully Explicitly within the Framework of the Generalized Positive Auxiliary Variable Approach (GPAV). Artificial Viscosity Stabilization that Modifies the Kinetic Energy is Introduced to Improve Accuracy of the GPAV Ensemble Methods. Numerical Results Are Presented to Demonstrate the Accuracy and Robustness of the Ensemble Algorithms.

Evaluating Ai Sentiment Analysis, Aakriti Shah

Honors Program Theses

This paper presents a comparative analysis of human and AI performance on a sentiment analysis task involving the coding of qualitative data from community program transcripts. The results demonstrate promising but imperfect agreement between two AI models, Claude and Bing, versus three human annotators and one expert annotator using the Community Capitals framework categories. While both models achieved fair alignment with human judgment, confusion patterns emerged involving metaphorical language and text overlapping multiple categories. The findings provide a case study for benchmarking conversational AI systems against human baselines to reveal limitations and target improvements. Key gaps center around distinguishing between …

Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty

Mathematics and Statistics Faculty Publications

In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the bicircular matroids with no U3,6-minor.

Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.

Applications For Functional Data Analysis, Kacy D. Kane

Graduate Research Theses & Dissertations

Functional Data Analysis is often used in the study of data that exists over a continuum, such as time. There are two datasets that will be considered here. For the first study we have a dataset on the efficacy of a lobectomy in reduction or elimination of epileptic seizures in patients. After an initial analysis of the dataset from a multinomial model perspective, we found that there were outliers in our dataset. From there, we considered a Multinomial Mixture Model to aid in the detection of outliers. In our second dataset we are considering a social robotics dataset where the …

Invasion Dynamics Of The European Collared-Dove In North America Are Explained By Combined Effects Of Habitat And Climate, Yiran Shao, Danielle Ethier, Simon Bonner

Statistical and Actuarial Sciences Publications

Global biodiversity is increasingly threatened by the spread of invasive species. Understanding the mechanisms influencing the initial colonization and persistence of invaders is therefore needed if conservation actions are to prevent new invasions or strive to slow their spread. The Eurasian Collared-Dove (Streptopelia decaocto, EUCO) is one of the most successful avian invasive species in North America; however, to our knowledge, no study has simultaneously examined the role that climate-matching, human activity, directional propagation, and local density have in this invasion process. Our research expands upon a cellular-automata-based hierarchical model developed to assess directional invasion dynamics to further quantify the …