Statistics and Probability Commons^™

A Bayesian Markov Chain Monte Carlo Approach To Uncertainty Quantification, Matthew Isaac

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Uncertainty quantification (UQ) is a framework used frequently in engineering analyses to understand how uncertainty in system inputs lead to uncertainty in the system output. An instability is observed in a UQ method proposed by Roy and Oberkampf and a Bayesian Markov Chain Monte Carlo approach to UQ is offered as an alternative. The Bayesian approach allows analysts to incorporate information from various available sources including observed measurements and expert opinion and to update the analysis and results as more information becomes available. An illustrative engineering example is provided as a platform to demonstrate the Bayesian UQ approach and to …

Integrating Data Science Ethics Into An Undergraduate Major, Benjamin Baumer, Randi L. Garcia, Albert Y. Kim, Katherine M. Kinnaird, Miles Q. Ott

Statistical and Data Sciences: Faculty Publications

We present a programmatic approach to incorporating ethics into an undergraduate major in statistical and data sciences. We discuss departmental-level initiatives designed to meet the National Academy of Sciences recommendation for weaving ethics into the curriculum from top-to-bottom as our majors progress from our introductory courses to our senior capstone course, as well as from side-to-side through co-curricular programming. We also provide six examples of data science ethics modules used in five different courses at our liberal arts college, each focusing on a different ethical consideration. The modules are designed to be portable such that they can be flexibly incorporated …

Pre-Testing Of The Who’S Educational Video: “How To Protect Yourself Against Covid-19”, Hilyatul Fadliyah, Manendra Muhtar, Munih Munih, Sylviasari Risgiantini, Weny Wulandary, Hadi Pratomo

Kesmas

The coronavirus disease 2019 (COVID-19) pandemic, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was declared a public health emergency in many countries, including Indonesia. The World Health Organization (WHO) released an educational video, entitled "How to Protect Yourself Against COVID-19", which explained how to prevent the spread of COVID-19. This study is a qualitative study that aims to pre-test this video, based on the Information, Education, Communication (IEC) theory, by analyzing teenagers’ perceptions of the video. The design used was a Rapid Assessment Procedure (RAP), and the data were collected by conducting in-depth interviews with participants, through …

Impact Of Lockdown In India: A Case Study Comparing Kanataka With International Model, Stelvin Sebastian, Aby Paul, Jeeva Joseph, Joel Joby, Sanjo Saijan, Jobin Kunjumon Vilapurathu

Kesmas

The COVID-19 was declared a pandemic and a global health emergency by WHO, prompting various countries to implement early and stringent social distancing protocols through lockdown, to flatten the epidemic curve. The objective of the present study was to assess the impacts and effectiveness of the lockdown protocol in Karnataka and Punjab, compared with the implementation of this method in Australia and the UK. This study involved the collection of data from different authorized databases, in two phases. The first phase included the time starting with the first-reported index case through the 14th day after the declaration of lockdown, for …

Review Of Trial Therapies And Treatment For Covid-19: Lessons For Indonesia, Halma Zahro Mukhlida, Hilma Hasro Maulida, Gunanti Khairunnisa, Margaretha Josephine Mantrono, Risky Kusuma Hartono, Rindu Rindu, Eka R W Purnamasari, Rizky Fajar Meirawan

Kesmas

The infectious disease from Coronavirus Disease 2019, or COVID-19, has quickly spread world-wide since 2019. Therapies for managing COVID-19 have yet to be confirmed as medication for the severe sickness that the disease may cause. This study aimed to review the previous research of the efficacy of trial therapy and treatment to the patients in the hospital with COVID-19. Using PRISMA guidelines as a method for conducting a systematic literature review, a total of 67 articles were collected from several online journal databases. Various therapies were found that are effective in the treatment and management of COVID-19. In accordance with …

Uniform Random Variate Generation With The Linear Congruential Method, Joseph Free

PANDION: The Osprey Journal of Research and Ideas

This report considers the issue of using a specific linear congruential generator (LCG) to create random variates from the uniform(0,1) distribution. The LCG is used to generate multiple samples of pseudo-random numbers and statistical computation techniques are used to assess whether those samples could have resulted from a uniform(0,1) distribution. Source code is included with this report in the appendix along with annotations.

Lectures On Mathematical Computing With Python, Jay Gopalakrishnan

PDXOpen: Open Educational Resources

This open resource is a collection of class activities for use in undergraduate courses aimed at teaching mathematical computing, and computational thinking in general, using the python programming language. It was developed for a second-year course (MTH 271) revamped for a new undergraduate program in data science at Portland State University. The activities are designed to guide students' use of python modules effectively for scientific computation, data analysis, and visualization.

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Even Order Ranked Set Sampling With Auxiliary Variable, Muhammad Tayyab, Muhammad Noor Ul-Amin, Muhammad Hanif

Journal of Modern Applied Statistical Methods

Even order ranked set sampling (EORSS) is a novel proposed ranked set sampling scheme connected with an auxiliary variable correlated with the study variable. This scheme quantifies only the one sampling unit which is at even position from each ranking set by employing specific criteria. The performance of the ratio estimator under EORSS is compared to its contemporary estimators in simple random sampling (SRS), ranked set sampling (RSS), median ranked set sampling (MRSS) and quartile ranked set sampling (QRSS) exploiting the same number of quantified units. The simulation results proved that EORSS is an efficient alternative sampling scheme for ratio …

Lattice Of Maximal-Primary Ideals In Quadratic Orders, Ryan Bridges

Mathematics & Statistics ETDs

An order is a subring of the ring of integers of an algebraic extension, Peruginelli and Zanardo classified the lattices of orders with prime index inside te ring of integers of quadratic extensions of the rational numbers. The lattices are quite striking and have different layered structure depending on whether the prime is inert, split, or ramified. This thesis considers the orders which have prime power index inside the Gaussian integers. This is a nice generalization of the work of Peruginelli and Zanardo, and succeeds in a few classifications of specific instances of orders derived from inert primes.

Objectives Driven Participatory Evaluation Model, Dustin R. Saalman

Journal of Modern Applied Statistical Methods

The ability to complete program evaluations of educational programming is typically restricted by the availability of resources, such as time, money and a trained evaluator. Although not a replacement for trained evaluators, promoting evaluative capacity and evaluative thinking within an organization can help mitigate this gap between talent and resources. Participatory evaluation is purported to increase organizational learning and promote evaluative thinking within an organization (Cousins & Whitmore, 1998). Objectives oriented evaluation is an easily understood evaluation method which provides a refined focus program outcome (Madaus & Stufflebeam, 1989). Using an internal evaluation of a new faculty onboarding course at …

Statistical Methodology To Establish A Benchmark For Evaluating Antimicrobial Resistance Genes Through Real Time Pcr Assay, Enakshy Dutta

Department of Statistics: Dissertations, Theses, and Student Research

Novel diagnostic tests are usually compared with gold standard tests for evaluating diagnostic accuracy. For assessing antimicrobial resistance (AMR) to bovine respiratory disease (BRD) pathogens, phenotypic broth microdilution method is used as gold standard (GS). The objective of the thesis is to evaluate the optimal cycle threshold (Ct) generated by real-time polymerase chain reaction (rtPCR) to genes that confer resistance that will translate to the phenotypic classification of AMR. Data from two different methodologies are assessed to identify Ct that will discriminate between resistance (R) and susceptibility (S). First, the receiver operating characteristic (ROC) curve was used to determine the …

Sars-Cov-2 Viral And Serological Testing When College Campuses Reopen: Some Practical Considerations, Isaac Chun-Hai Fung, Chi-Ngai Cheung, Andreas Handel

Biostatistics, Epidemiology & Environmental Health Sciences: Faculty Publications

The coronavirus disease 2019 (COVID-19) pandemic prompted universities across the United States to close campuses in Spring 2020. Universities are deliberating whether, when, and how they should resume in-person instruction in Fall 2020. In this essay, we discuss some practical considerations for the use of 2 potentially useful control strategies based on testing: (1) severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reverse transcriptase-polymerase chain reaction (RT-PCR) testing followed by case-patient isolation and quarantine of close contacts, and (2) serological testing followed by an “immune shield” approach, that is, low social distancing requirements for seropositive persons. The isolation of case-patients and …

Maximum Likelihood Estimations Based On Upper Record Values For Probability Density Function And Cumulative Distribution Function In Exponential Family And Investigating Some Of Their Properties, Saman Hosseini, Parviz Nasiri, Sharad Damodar Gore

Journal of Modern Applied Statistical Methods

A useful subfamily of the exponential family is considered. The ML estimation based on upper record values are calculated for the parameter, Cumulative Density Function, and Probability Density Function of the subfamily. The relationship between MLE based on record values and a random sample are discussed, along with some properties of these estimators, and its utility is shown for large samples.

Maintaining Rich Dialogic Interactions In The Transition To Synchronous Online Learning, Hyunyi Jung, Corey Brady

Mathematical and Statistical Science Faculty Research and Publications

A central premise across a variety of educational research and policy documents is that students learn with greater understanding in classrooms where they engage in exploring, reasoning, and communicating about their thinking (Hiebert and Wearne, 1993; National Council of Teachers of English, 2016; National Council of Teachers of Mathematics, 2000). With the recent emergency transition to remote online instruction in higher education, opportunities for rich synchronous learning have been diminished in many courses. Most instructors have had to adapt rapidly from in-person classroom settings to online environments without sufficient time and training. Accordingly, college students have shared concerns about the …

The Comparison Between Maximum Weighted And Trimmed Likelihood Estimator Of The Simple Circular Regression Model, Ehab A. Mahmood, Habshah Midi, Abdul Ghapor Hussin

Journal of Modern Applied Statistical Methods

The Maximum Likelihood Estimator (MLE) was used to estimate unknown parameters of the simple circular regression model. However, it is very sensitive to outliers in data set. A robust method to estimate model parameters is proposed.

Bayesian Estimation Of The Parameters Of Discrete Weibull Type (I) Distribution, Samir Kamel Ashour, Mohamed Salem Abdelwahab Muiftah

Journal of Modern Applied Statistical Methods

Bayesian estimation of the continuous Weibull distribution parameters was studied by Ahmad and Ahmad (2013) under the assumption of knowing the shape parameter. Bayesian estimates are considered here of the parameters of the discrete Weibull Type I [DW(I)] distribution and are obtained under two different assumptions: when the shape parameter is known, and when both parameters are independent random variables. A Mathcad program is performed to simulate data from the DW(I) distribution considering different values of the parameters and different sample sizes, and to obtain Bayesian parameter estimates. The resulted estimates are compared to the ML and proportion estimates obtained …

Hoop Dreams: An Empirical Analysis Of The Gender Wage Gap In Professional Basketball, Hailey Dicicco

Business and Economics Presentations

The gender wage gap is a very prominent point of discussion in the professional world, but in the sports world, it has taken the spotlight in recent years. One sport that has seen discussion and debate over salary differences is the National Basketball Association and Women’s National Basketball Association. In 2018, the average salary in the NBA was 6.4 million dollars, while the average salary in the WNBA was 71,635 dollars. A reason why these salaries are so differently is due to the amount of revenue that each league brings in. The NBA brings in roughly 7.4 billion dollars a …

"A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen

Mathematics & Statistics ETDs

In this thesis, I studied a newly developed variable selection method SODA, and three customarily used variable selection methods: LASSO, Elastic net, and Random forest for environmental mixture data. The motivating datasets have neuro-developmental status as responses and metal measurements and demographic variables as covariates. The challenges for variable selections include (1) many measured metal concentrations are highly correlated, (2) there are many possible ways of modeling interactions among the metals, (3) the relationships between the outcomes and explanatory variables are possibly nonlinear, (4) the signal to noise ratio in the real data may be low. To compare these methods …

The Logic Model, Participatory Evaluation And Out Of School Art Programs, Kimberly A. Kleinhans

Journal of Modern Applied Statistical Methods

The logic model and participatory evaluation are two popular methods of conducting program evaluation. Although both methods have their strengths, each has distinct weaknesses which can be ameliorated by combining them both together. The combined method is used to evaluate an out of school art program at a museum. Using both the logic model and participatory evaluation yielded beneficial results with more accurate representation of program outcomes.

Quantitatively Motivated Model Development Framework: Downstream Analysis Effects Of Normalization Strategies, Jessica M. Rudd

Doctor of Data Science and Analytics Dissertations

Through a review of epistemological frameworks in social sciences, history of frameworks in statistics, as well as the current state of research, we establish that there appears to be no consistent, quantitatively motivated model development framework in data science, and the downstream analysis effects of various modeling choices are not uniformly documented. Examples are provided which illustrate that analytic choices, even if justifiable and statistically valid, have a downstream analysis effect on model results. This study proposes a unified model development framework that allows researchers to make statistically motivated modeling choices within the development pipeline. Additionally, a simulation study is …

Utility Of Inflammatory Markers To Predict Adverse Outcome In Acute Pancreatitis: A Retrospective Study In A Single Academic Center, Mohamad Mubder, Banreet Dhindsa, Danny Nguyen, Syed Saghir, Chad Cross, Ranjit Makar, Gordon Ohning

School of Medicine Faculty Research

Background/Aim: Acute pancreatitis (AP) is a commonly encountered emergency where early identification of complicated cases is important. Inflammatory markers like lymphocyte to monocyte ratio (LMR) and neutrophil to lymphocyte ratio (NLR) are simple and readily available markers. In this study, we evaluated the utility of these markers in the early identification of patients with complicated AP. Patients and Methods: All patients with a diagnosis of AP admitted to the University Medical Center in Las Vegas/Nevada between August 2015 and September 2018 were identified using ICD-10 codes. Medical records were reviewed retrospectively. Epidemiological measures and their associated confidence intervals were calculated …

On The Noisy Gradient Descent That Generalizes As Sgd, Jingfeng Wu, Wenqing Hu, Haoyi Xiong, Jun Huan, Vladimir Braverman, Zhanxing Zhu

Mathematics and Statistics Faculty Research & Creative Works

The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and covariance structure of gradient noise are critical for regularization, it remains unclear whether or not the class of noise distributions is important. In this work we provide negative results by showing that noises in classes different from the SGD noise can also effectively regularize gradient descent. Our finding is based on a novel observation on the structure of the SGD noise: it is the multiplication of the gradient matrix and a …

A Generalized Family Of Lifetime Distributions And Survival Models, Mahmoud Aldeni, Felix Famoye, Carl Lee

Journal of Modern Applied Statistical Methods

In lifetime data, the hazard function is a common technique for describing the characteristics of lifetime distribution. Monotone increasing or decreasing, and unimodal are relatively simple hazard function shapes, which can be modeled by many parametric lifetime distributions. However, fewer distributions are capable of modeling diverse and more complicated shapes such as N-shaped, reflected N-shaped, W-shaped, and M-shaped hazard rate functions. A generalized family of lifetime distributions, the uniform-R{generalized lambda} (U-R{GL}) are introduced and the corresponding survival models are derived, and applied to two lifetime data sets. The survival model is applied to a right censored lifetime data set.

A Revised Logic Model For Educational Program Evaluation, Zsa-Zsa Booker

Journal of Modern Applied Statistical Methods

The logic model is an evaluation tool popularly used for obtaining grant funding. Its limitations make it unlike other theory driven evaluation methods. A critical examination of the logic model leads to the construction of an enriched revised logic model.

Forward And Backward Continuation Ratio Models For Ordinal Response Variables, Xing Liu, Haiyan Bai

Journal of Modern Applied Statistical Methods

There are different types of continuation ratio (CR) models for ordinal response variables. The different model equations, corresponding parameterizations, and nonequivalent results are confusing. The purpose of this study is to introduce different types of forward and backward CR models, demonstrate how to implement these models using Stata, and compare the results using data from the Educational Longitudinal Study of 2002 (ELS:2002).

Identifying Which Of J Independent Binomial Distributions Has The Largest Probability Of Success, Rand Wilcox

Journal of Modern Applied Statistical Methods

Let p₁,…, p_J denote the probability of a success for J independent random variables having a binomial distribution and let p₍₁₎ ≤ … ≤ p_(J) denote these probabilities written in ascending order. The goal is to make a decision about which group has the largest probability of a success, p_(J). Let p̂₁,…, p̂_J denote estimates of p₁,…,p_J, respectively. The strategy is to test J − 1 hypotheses comparing the group with the largest estimate to each of the J − 1 …

Jmasm 53: Miccerird, Michael Lance

Journal of Modern Applied Statistical Methods

Fortran 77 and 90 modules (REALPOPS.lib) exist for invoking the 8 distributions estimated by Micceri (1989). These respective modules were created by Sawilowsky et al. (1990) and Sawilowsky and Fahoome (2003). The MicceriRD (Micceri’s Real Distributions) Python package was created because Python is increasingly used for data analysis and, in some cases, Monte Carlo simulations.

Bayesian Analysis Of Extended Cox Model With Time-Varying Covariates Using Bootstrap Prior, Oyebayo R. Olaniran, Mohd Asrul A. Abdullah

Journal of Modern Applied Statistical Methods

A new Bayesian estimation procedure for extended cox model with time varying covariate was presented. The prior was determined using bootstrapping technique within the framework of parametric empirical Bayes. The efficiency of the proposed method was observed using Monte Carlo simulation of extended Cox model with time varying covariates under varying scenarios. Validity of the proposed method was also ascertained using real life data set of Stanford heart transplant. Comparison of the proposed method with its competitor established appreciable supremacy of the method.

Regression: Determining Which Of P Independent Variables Has The Largest Or Smallest Correlation With The Dependent Variable, Plus Results On Ordering The Correlations Winsorized, Rand Wilcox

Journal of Modern Applied Statistical Methods

In a regression context, consider p independent variables and a single dependent variable. The paper addresses two goals. The first is to determine the extent it is reasonable to make a decision about whether the largest estimate of the Winsorized correlations corresponds to the independent variable that has the largest population Winsorized correlation. The second is to determine the extent it is reasonable to decide that the order of the estimates of the Winsorized correlations correctly reflects the true ordering. Both goals are addressed by testing relevant hypotheses. Results in Wilcox (in press a) suggest using a multiple comparisons procedure …

Jmasm 52: Extremely Efficient Permutation And Bootstrap Hypothesis Tests Using R, Christina Chatzipantsiou, Marios Dimitriadis, Manos Papadakis, Michail Tsagris

Journal of Modern Applied Statistical Methods

Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. Computationally efficient method for calculating permutation-based p-values for the Pearson correlation coefficient and two independent samples t-test are proposed. The method is general and can be applied to other similar two sample mean or two mean vectors cases.