# Statistics and Probability Commons™

Articles 1 - 30 of 12116

## Full-Text Articles in Statistics and Probability

"A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen 4785403, Paul-Yvann Djamen Jul 2020

#### "A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen 4785403, 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 ...

Comparing Means Under Heteroscedasticity And Nonnormality: Further Exploring Robust Means Modeling, Alyssa Counsell, Robert Philip Chalmers, Robert A. Cribbie Jun 2020

#### Comparing Means Under Heteroscedasticity And Nonnormality: Further Exploring Robust Means Modeling, Alyssa Counsell, Robert Philip Chalmers, Robert A. Cribbie

##### Journal of Modern Applied Statistical Methods

Comparing the means of independent groups is a concern when the assumptions of normality and variance homogeneity are violated. Robust means modeling (RMM) was proposed as an alternative to ANOVA-type procedures when the assumptions of normality and variance homogeneity are violated. The purpose of this study is to compare the Type I error and power rates of RMM to the trimmed Welch procedure. A Monte Carlo study was used to investigate RMM and the trimmed Welch procedure under several conditions of nonnormality and variance heterogeneity. The results suggest that the trimmed Welch provides a better balance of Type I error ...

#### Inferences About The Probability Of Success, Given The Value Of A Covariate, Using A Nonparametric Smoother, Rand Wilcox

##### Journal of Modern Applied Statistical Methods

For a binary random variable Y, let p(x) = P(Y = 1 | X = x) for some covariate X. The goal of computing a confidence interval for p(x) is considered. In the logistic regression model, even a slight departure difficult to detect via a goodness-of-fit test can yield inaccurate results. The accuracy of a confidence interval can deteriorate as the sample size increases. The goal is to suggest an alternative approach based on a smoother, which provides a more flexible approximation of p(x).

Jun 2020

#### A Note On Inferences About The Probability Of Success, Rand Wilcox

##### Journal of Modern Applied Statistical Methods

There is an extensive literature dealing with inferences about the probability of success. A minor goal in this note is to point out when certain recommended methods can be unsatisfactory when the sample size is small. The main goal is to report results on the two-sample case. Extant results suggest using one of four methods. The results indicate when computing a 0.95 confidence interval, two of these methods can be more satisfactory when dealing with small sample sizes.

At The Interface Of Algebra And Statistics, Tai-Danae Bradley Jun 2020

#### At The Interface Of Algebra And Statistics, Tai-Danae Bradley

##### All Dissertations, Theses, and Capstone Projects

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals ...

Research In Short Term Actuarial Modeling, Elijah Howells Jun 2020

#### Research In Short Term Actuarial Modeling, Elijah Howells

##### Electronic Theses, Projects, and Dissertations

This paper covers mathematical methods used to conduct actuarial analysis in the short term, such as policy deductible analysis, maximum covered loss analysis, and mixtures of distributions. Assessment of a loss variable's distribution under the effect of a policy deductible, as well as one with an implemented maximum covered loss, and under both a policy deductible and maximum covered loss will also be covered. The derivation, meaning, and use of cost per loss and cost per payment will be discussed, as will those of an aggregate sum distribution, stop loss policy, and maximum likelihood estimation. For each topic, special ...

Integrated Multiple Mediation Analysis: A Robustness–Specificity Trade-Off In Causal Structure, An-Shun Tai, Sheng-Hsuan Lin May 2020

#### Integrated Multiple Mediation Analysis: A Robustness–Specificity Trade-Off In Causal Structure, An-Shun Tai, Sheng-Hsuan Lin

##### Harvard University Biostatistics Working Paper Series

Recent methodological developments in causal mediation analysis have addressed several issues regarding multiple mediators. However, these developed methods differ in their definitions of causal parameters, assumptions for identification, and interpretations of causal effects, making it unclear which method ought to be selected when investigating a given causal effect. Thus, in this study, we construct an integrated framework, which unifies all existing methodologies, as a standard for mediation analysis with multiple mediators. To clarify the relationship between existing methods, we propose four strategies for effect decomposition: two-way, partially forward, partially backward, and complete decompositions. This study reveals how the direct and ...

Waiting-Time Paradox In 1922, Naoki Masuda, Takayuki Hiraoka May 2020

#### Waiting-Time Paradox In 1922, Naoki Masuda, Takayuki Hiraoka

##### Northeast Journal of Complex Systems (NEJCS)

We present an English translation and discussion of an essay that a Japanese physicist, Torahiko Terada, wrote in 1922. In the essay, he described the waiting-time paradox, also called the bus paradox, which is a known mathematical phenomenon in queuing theory, stochastic processes, and modern temporal network analysis. He also observed and analyzed data on Tokyo City trams to verify the relevance of the waiting-time paradox to busy passengers in Tokyo at the time. This essay seems to be one of the earliest documentations of the waiting-time paradox in a sufficiently scientific manner.

Metabolomic Profiling Of Nicotiana Spp. Nectars Indicate That Pollinator Feeding Preference Is A Stronger Determinant Than Plant Phylogenetics In Shaping Nectar Diversity, Fredy A. Silva, Elizabeth C. Chatt, Siti-Nabilla Mahalim, Adel Guirgis, Xingche Guo, Dan S. Nettleton, Basil J. Nikolau, Robert W. Thornburg May 2020

#### Metabolomic Profiling Of Nicotiana Spp. Nectars Indicate That Pollinator Feeding Preference Is A Stronger Determinant Than Plant Phylogenetics In Shaping Nectar Diversity, Fredy A. Silva, Elizabeth C. Chatt, Siti-Nabilla Mahalim, Adel Guirgis, Xingche Guo, Dan S. Nettleton, Basil J. Nikolau, Robert W. Thornburg

##### Statistics Publications

Floral nectar is a rich secretion produced by the nectary gland and is offered as reward to attract pollinators leading to improved seed set. Nectars are composed of a complex mixture of sugars, amino acids, proteins, vitamins, lipids, organic and inorganic acids. This composition is influenced by several factors, including floral morphology, mechanism of nectar secretion, time of flowering, and visitation by pollinators. The objective of this study was to determine the contributions of flowering time, plant phylogeny, and pollinator selection on nectar composition in Nicotiana. The main classes of nectar metabolites (sugars and amino acids) were quantified using gas ...

On Statistical Significance Of Discriminant Function Coefficients, Tolulope T. Sajobi, Gordon H. Fick, Lisa M. Lix May 2020

#### On Statistical Significance Of Discriminant Function Coefficients, Tolulope T. Sajobi, Gordon H. Fick, Lisa M. Lix

##### Journal of Modern Applied Statistical Methods

Discriminant function coefficients are useful for describing group differences and identifying variables that distinguish between groups. Test procedures were compared based on asymptotically approximations, empirical, and exact distributions for testing hypotheses about discriminant function coefficients. These tests are useful for assessing variable importance in multivariate group designs.

May 2020

#### Sensitivity Analysis For Incomplete Data And Causal Inference, Heng Chen

##### Statistical Science Theses and Dissertations

In this dissertation, we explore sensitivity analyses under three different types of incomplete data problems, including missing outcomes, missing outcomes and missing predictors, potential outcomes in \emph{Rubin causal model (RCM)}. The first sensitivity analysis is conducted for the \emph{missing completely at random (MCAR)} assumption in frequentist inference; the second one is conducted for the \emph{missing at random (MAR)} assumption in likelihood inference; the third one is conducted for one novel assumption, the sixth assumption'' proposed for the robustness of instrumental variable estimand in causal inference.

Statistical Models And Analysis Of Univariate And Multivariate Degradation Data, Lochana Palayangoda May 2020

#### Statistical Models And Analysis Of Univariate And Multivariate Degradation Data, Lochana Palayangoda

##### Statistical Science Theses and Dissertations

For degradation data in reliability analysis, estimation of the first-passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571-590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this thesis, we propose improved techniques based on saddlepoint approximation, which enhance upon their suggested methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible ...

#### Evaluation Of The Utility Of Informative Priors In Bayesian Structural Equation Modeling With Small Samples, Hao Ma

##### Department of Education Policy and Leadership Theses and Dissertations

The estimation of parameters in structural equation modeling (SEM) has been primarily based on the maximum likelihood estimator (MLE) and relies on large sample asymptotic theory. Consequently, the results of the SEM analyses with small samples may not be as satisfactory as expected. In contrast, informative priors typically do not require a large sample, and they may be helpful for improving the quality of estimates in the SEM models with small samples. However, the role of informative priors in the Bayesian SEM has not been thoroughly studied to date. Given the limited body of evidence, specifying effective informative priors remains ...

#### Statistical Inference Of Adaptation At Multiple Genomic Scales Using Supervised Classification And A Hidden Markov Model, Lauren A. Sugden

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

An Improved Two Independent-Samples Randomization Test For Single-Case Ab-Type Intervention Designs: A 20-Year Journey, Joel R. Levin, John M. Ferron, Boris S. Gafurov May 2020

#### An Improved Two Independent-Samples Randomization Test For Single-Case Ab-Type Intervention Designs: A 20-Year Journey, Joel R. Levin, John M. Ferron, Boris S. Gafurov

##### Journal of Modern Applied Statistical Methods

Detailed is a 20-year arduous journey to develop a statistically viable two-phase (AB) single-case two independent-samples randomization test procedure. The test is designed to compare the effectiveness of two different interventions that are randomly assigned to cases. In contrast to the unsatisfactory simulation results produced by an earlier proposed randomization test, the present test consistently exhibited acceptable Type I error control under various design and effect-type configurations, while at the same time possessing adequate power to detect moderately sized intervention-difference effects. Selected issues, applications, and a multiple-baseline extension of the two-sample test are discussed.

Support Vector Machine-Based Modified Sp Statistic For Subset Selection With Non-Normal Error Terms, Shivaji Shripati Desai, D N. Kashid May 2020

#### Support Vector Machine-Based Modified Sp Statistic For Subset Selection With Non-Normal Error Terms, Shivaji Shripati Desai, D N. Kashid

##### Journal of Modern Applied Statistical Methods

Support vector machine (SVM) is used for estimation of regression parameters to modify the sum of cross products (Sp). It works well for some nonnormal error distributions. The performance of existing robust methods and the modified Sp is evaluated through simulated and real data. The results show the performance of the modified Sp is good.

Recurrence Relations For Marginal And Joint Moment Generating Functions Of Topp-Leone Generated Exponential Distribution Based On Record Values And Its Characterization, Zaki Anwar, Neetu Gupta, Mohd Akram Raza Khan, Qazi Azhad Jamal May 2020

#### Recurrence Relations For Marginal And Joint Moment Generating Functions Of Topp-Leone Generated Exponential Distribution Based On Record Values And Its Characterization, Zaki Anwar, Neetu Gupta, Mohd Akram Raza Khan, Qazi Azhad Jamal

##### Journal of Modern Applied Statistical Methods

The exact expressions and some recurrence relations are derived for marginal and joint moment generating functions of kth lower record values from Topp-Leone Generated (TLG) Exponential distribution. This distribution is characterized by using the recurrence relation of the marginal moment generating function of kth lower record values.

#### A New Exponential Approach For Reducing The Mean Squared Errors Of The Estimators Of Population Mean Using Conventional And Non-Conventional Location Parameters, Housila P. Singh, Anita Yadav

##### Journal of Modern Applied Statistical Methods

Classes of ratio-type estimators t (say) and ratio-type exponential estimators te (say) of the population mean are proposed, and their biases and mean squared errors under large sample approximation are presented. It is the class of ratio-type exponential estimators te provides estimators more efficient than the ratio-type estimators.

May 2020

#### Decision Tree For Predicting The Party Of Legislators, Afsana Mimi

##### Publications and Research

The motivation of the project is to identify the legislators who voted frequently against their party in terms of their roll call votes using Office of Clerk U.S. House of Representatives Data Sets collected in 2018 and 2019. We construct a model to predict the parties of legislators based on their votes. The method we used is Decision Tree from Data Mining. Python was used to collect raw data from internet, SAS was used to clean data, and all other calculations and graphical presentations are performed using the R software.

May 2020

#### First-Year Computer Science Students: Pathways And Perceptions In Introductory Computer Science Courses, Christina A. Leblanc

##### Electronic Theses and Dissertations

This study examined student perceptions and experiences of an introductory Computer Science course at the University of Maine; COS 125: Introduction to Problem Solving Using Computer Programs. It also explored the pathways that students pursue after taking COS 125, depending on their success in the course, and their motivation to persist. Through characterizing student populations and their performance in their first semester in the Computer Science program, they can be placed into one of three categories that explain their path; a “continuer” (passed COS 125 and decided to stay in the major), a “persister” (did not pass COS 125 and ...

Using Stability To Select A Shrinkage Method, Dean Dustin May 2020

#### Using Stability To Select A Shrinkage Method, Dean Dustin

##### Dissertations and Theses in Statistics

Shrinkage methods are estimation techniques based on optimizing expressions to find which variables to include in an analysis, typically a linear regression. The general form of these expressions is the sum of an empirical risk plus a complexity penalty based on the number of parameters. Many shrinkage methods are known to satisfy an ‘oracle’ property meaning that asymptotically they select the correct variables and estimate their coefficients efficiently. In Section 1.2, we show oracle properties in two general settings. The first uses a log likelihood in place of the empirical risk and allows a general class of penalties. The ...

Ragweed And Sagebrush Pollen Can Distinguish Between Vegetation Types At Broad Spatial Scales, Hannah M. Carroll, Alan D. Wanamaker, Lynn G. Clark, Brian J. Wilsey May 2020

#### Ragweed And Sagebrush Pollen Can Distinguish Between Vegetation Types At Broad Spatial Scales, Hannah M. Carroll, Alan D. Wanamaker, Lynn G. Clark, Brian J. Wilsey

##### Ecology, Evolution and Organismal Biology Publications

Patterns of vegetation distribution at regional to subcontinental scales can inform understanding of climate. Delineating ecoregion boundaries over geologic time is complicated by the difficulty of distinguishing between prairie types at broad spatial scales using the pollen record. Pollen ratios are sometimes employed to distinguish between vegetation types, although their applicability is often limited to a geographic range. The Neotoma Paleoecology Database offers an unparalleled opportunity to synthesize a large number of pollen datasets. Ambrosia (ragweed) is a genus of mesic‐adapted species sensitive to summer moisture. Artemisia (sagebrush, wormwood, mugwort) is a genus of dry‐mesic‐adapted species resilient ...

#### The Effects Of Zoledronate And Sleep Deprivation On The Distal Femur Trabecular Thickness Of Ovariectomized Rats: Application Of Different Statistical Methods, Erin Nolte

##### Student Scholar Symposium Abstracts and Posters

Osteoporosis is a disease that causes the degradation of bone, leading to an increased risk of fracture. 1 in 3 women over the age of 50 will be affected by Osteoporosis. This study aims to understand how bone is affected by sleep deprivation in estrogen-deficient rats, and how Zoledronate might negate the inimical effects of sleep deprivation on bone. As bone mineral density (BMD) is a crude evaluation of the architectural changes seen in Osteoporosis, trabecular thickness may serve as a better single evaluation of bone health. 31 Wistar female rats were ovariectomized and separated into 4 random groups. The ...

Life And Death: Quantifying The Risk Of Heart Disease With Machine Learning, Jack Scott Glienke May 2020

#### Life And Death: Quantifying The Risk Of Heart Disease With Machine Learning, Jack Scott Glienke

##### Honors Program Theses

Coronary heart disease has long been a key area of focus in the discussion of public health. As such, numerous studies have been conducted throughout history with the sole intention of identifying risk factors leading to the onset of cardiovascular conditions. A plethora of statistical procedures can be used to identify an individual’s risk of developing heart disease, yet regression models tend to be the default tool used by researchers. Using the data obtained from the most influential cardiovascular study to date, the Framingham Heart Study, this analysis uses machine learning techniques to generate and test the predictive power ...

Gait Characterization Using Computer Vision Video Analysis, Martha T. Gizaw May 2020

#### Gait Characterization Using Computer Vision Video Analysis, Martha T. Gizaw

The World Health Organization reports that falls are the second-leading cause of accidental death among senior adults around the world. Currently, a research team at William & Mary’s Department of Kinesiology & Health Sciences attempts to recognize and correct aging-related factors that can result in falling. To meet this goal, the members of that team videotape walking tests to examine individual gait parameters of older subjects. However, they undergo a slow, laborious process of analyzing video frame by video frame to obtain such parameters. This project uses computer vision software to reconstruct walking models from residents of an independent living retirement ...

May 2020

#### Modeling Movement: A Machine-Learning Approach To Track Migration Routes After Displacement, Ethan Harrison

Over the past decade, the number of individuals internally displaced by conflict (IDPs) has reached unprecedented levels. Humanitarian actors and first-responders face persistent information gaps in meeting the needs of these populations. Specifically, they face challenges in understanding where and how IDPs move after they are displaced, which is necessary to locate them in conflict-affected situations and provide them with life-saving assistance. In this paper, I propose a framework, using established machine-learning methods, to forecast the migration routes of these displaced populations (Chapter 1). In a case study of displacement in Yemen, my models predict 80% of IDPs' migration routes ...

#### 'Lmshapemaker': Utilizing The 'Rmapshaper' R Package To Modify Shapefiles For Use In Linked Micromap Plots, Braden D. Probst

##### All Graduate Theses and Dissertations

In order to effectively create map-based visualizations, some map modifications need to be conducted to ensure the map is readable and interpretable. There are several issues that need to be addressed to achieve this. The boundaries of a country may be overly complex which is particularly true with coastal areas of countries. Regions may be small and not seen in the final plot, as is the case with many capital cities in the world’s countries such as Washington D.C. and the Federal District of Mexico City. In other countries, regions may geographically lie far away from the rest ...

#### Predicting Disease Progression Using Deep Recurrent Neural Networks And Longitudinal Electronic Health Record Data, Seunghwan Kim

##### Engineering and Applied Science Theses & Dissertations

Electronic Health Records (EHR) are widely adopted and used throughout healthcare systems and are able to collect and store longitudinal information data that can be used to describe patient phenotypes. From the underlying data structures used in the EHR, discrete data can be extracted and analyzed to improve patient care and outcomes via tasks such as risk stratification and prospective disease management. Temporality in EHR is innately present given the nature of these data, however, and traditional classification models are limited in this context by the cross- sectional nature of training and prediction processes. Finding temporal patterns in EHR is ...

May 2020

#### Applications Of Machine Learning In High-Frequency Trade Direction Classification, Jared E. Hansen

##### All Graduate Theses and Dissertations

The correct assignment of trades as buyer-initiated or seller-initiated is paramount in many quantitative finance studies. Simple decision rule methods have been used for signing trades since many data sets available to researchers do not include the sign of each trade executed. By utilizing these decision rule methods, as well as engineering new variables from available data, we have demonstrated that machine learning models outperform prior methods for accurately signing trades as buys and sells, achieving state-of-the-art results. The best model developed was 4.5 percentage points more accurate than older methods when predicting onto unseen data. Since finance and ...

Introduction To Research Statistical Analysis: An Overview Of The Basics, Christian Vandever Apr 2020

#### Introduction To Research Statistical Analysis: An Overview Of The Basics, Christian Vandever

##### HCA Healthcare Journal of Medicine

This article covers many statistical ideas essential to research statistical analysis. Sample size is explained through the concepts of statistical significance level and power. Variable types and definitions are included to clarify necessities for how the analysis will be interpreted. Categorical and quantitative variable types are defined, as well as response and predictor variables. Statistical tests described include t-tests, ANOVA and chi-square tests. Multiple regression is also explored for both logistic and linear regression. Finally, the most common statistics produced by these methods are explored.