Statistics and Probability Commons^™

Non-Invasive Analysis Of The Sputum Transcriptome Discriminates Clinical Phenotypes Of Asthma, Xiting Yan

Yale Day of Data

Whole transcriptome wide gene expression profiles in the sputum and circulation from 100 asthma patients were measured using the Affymetrix HuGene 1.0ST arrays. Unsupervised clustering analysis based on pathways from KEGG were used to identify TEA clusters of patients from the sputum gene expression profiles. The identified TEA clusters have significantly different pre-bronchodilator FEV1, bronchodilator responsiveness, exhaled nitric oxide levels, history of hospitalization for asthma and history of intubation. Evaluation of TEA clusters in children from Asthma BRIDGE cohort confirmed the identified differences in intubation and hospitalization. Furthermore, evaluation of the TH2 gene signatures suggested a much lower prevalence of …

A Novel Pathway-Based Distance Score Enhances Assessment Of Disease Heterogeneity In Gene Expression, Yunqing Liu, Xiting Yan

Yale Day of Data

Distance-based unsupervised clustering of gene expression data is commonly used to identify heterogeneity in biologic samples. However, high noise levels in gene expression data and the relatively high correlation between genes are often encountered, so traditional distances such as Euclidean distance may not be effective at discriminating the biological differences between samples. In this study, we developed a novel computational method to assess the biological differences based on pathways by assuming that ontologically defined biological pathways in biologically similar samples have similar behavior. Application of this distance score results in more accurate, robust, and biologically meaningful clustering results in both …

Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam

Department of Math & Statistics Faculty Publications

Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure …

Ample Provision: A Preliminary Study Relating Budget Composition And High School Graduation Rates In Select Washington State Public School Districts, Gregory P. Gadow

All Undergraduate Projects

How to allocate scarce resources for an optimal outcome is of keen interest to those who set the budgets in public education. Simply throwing money at schools is not enough; it is important that money is spent where it will do the most good. This study considers Washington State public school districts and examines how the share of per-student expenditures in seven budget categories relates to on-time high school graduation rates. It is an investigative study, exploring whether there is enough evidence to merit further, more in-depth research. Using budget and graduation information from academic years 1997-98 through 2016-17 for …

Extensions Of Schauder's And Darbo's Fixed Point Theorems, Zhaocai Hao, Martin Bohner, Junjun Wang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, some new extensions of Schauder's and Darbo's fixed point theorems are given. As applications of the main results, the existence of global solutions for first-order nonlinear integro-differential equations of mixed type in a real Banach space is investigated.

Variance Estimation In Inverse Probability Weighted Cox Models, Di Shu, Jessica G. Young, Sengwee Toh, Rui Wang

Harvard University Biostatistics Working Paper Series

Inverse probability weighted Cox models can be used to estimate marginal hazard ratios under different treatments interventions in observational studies. To obtain variance estimates, the robust sandwich variance estimator is often recommended to account for the induced correlation among weighted observations. However, this estimator does not incorporate the uncertainty in estimating the weights and tends to overestimate the variance, leading to inefficient inference. Here we propose a new variance estimator that combines the estimation procedures for the hazard ratio and weights using stacked estimating equations, with additional adjustments for the sum of non-independent and identically distributed terms in a Cox …

General Approach Of Causal Mediation Analysis With Causally Ordered Multiple Mediators And Survival Outcome, An-Shun Tai, Pei-Hsuan Lin, Yen-Tsung Huang, Sheng-Hsuan Lin

Harvard University Biostatistics Working Paper Series

Causal mediation analysis with multiple mediators (causal multi-mediation analysis) is critical in understanding why an intervention works, especially in medical research. Deriving the path-specific effects (PSEs) of exposure on the outcome through a certain set of mediators can detail the causal mechanism of interest. However, the existing models of causal multi-mediation analysis are usually restricted to partial decomposition, which can only evaluate the cumulative effect of several paths. Moreover, the general form of PSEs for an arbitrary number of mediators has not been proposed. In this study, we provide a generalized definition of PSE for partial decomposition (partPSE) and for …

Missing Data Augmentation For Bayesian Multiplex Ergms, Robert Krause, Alberto Caimo

Conference papers

In this paper we present an estimation algorithm for Bayesian multiplex exponential random graphs (BmERGMs) under missing net- work data. Social actors are often connected with more than one type of relation, thus forming a multiplex network. It is important to consider these multiplex structures simultaneously when analyzing a multiplex network. The importance of proper models of multiplex network structures is even more pronounced under the issue of missing network data. The proposed algorithm is able to estimate BmERGMs under missing data and can be used to obtain proper multiple imputations for multiplex network structures. It is an extension of …

Comparative Analysis Of Students’ Performance Between Online And On Campus In An Introductory Statistics Course, Kendal Mcdonald

The Corinthian

In this research, we compare students’ performance in an online and on-campus introductory statistics and probability course at Georgia College. MyStatLab is the learning management system used in both the online and on-campus courses for homework and quizzes. The online data is produced by five summer courses between Summer 2014 to Summer 2017 and the on-campus data is produced from nine on-campus courses from Spring 2014, Spring 2016, and Spring 2017. For homework, the research compares the scores made between online and on-campus. For quizzes, we test if there is a difference between the scores and the number of attempts …

Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick

Theses, Dissertations and Capstones

In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S ² ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, V^ˆ (S ² ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.

Comparison Of Long-Term Survival Of Patients With Early-Stage Non–Small Cell Lung Cancer After Surgery Vs Stereotactic Body Radiotherapy, Alexander Chi, Wei Fang, Yeping Sun, Sinjin Wen

Faculty & Staff Scholarship

IMPORTANCE Previous comparisons of surgery and stereotactic body radiotherapy (SBRT) for early-stage (ES) non–small cell lung cancer (NSCLC) did not account for the extent of regional lymph node examination (LNE) during surgery. OBJECTIVE To compare long-term overall survival (OS) of patients with ES NSCLC after surgery vs SBRT when the extent of regional LNE in patients undergoing surgery is thoroughly considered. DESIGN, SETTING, AND PARTICIPANTS Cohort study with survival comparisons using the multivariable Cox proportional hazards model and after propensity score matching. Data from the National Cancer Database were analyzed from October 28, 2018, through April 18, 2019. Patients with …

Estimation Of Multivariate Asset Models With Jumps, Angela Loregian, Laura Ballotta, Gianluca Gianluca Fusai, Marcos Fabricio Perez

Business Faculty Publications

We propose a consistent and computationally efficient two-step methodology for the estimation of multidimensional non-Gaussian asset models built using Levy processes. The proposed framework allows for dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets as it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail …

The Principal Problem With Principal Components Regression, Gary N. Smith, Heidi Margaret Artigue

Pomona Economics

No abstract provided.

Cost-Effective Surveillance For Infectious Diseases Through Specimen Pooling And Multiplex Assays, Christopher Bilder, Joshua Tebbs, Christopher Mcmahan

Department of Statistics: Faculty Publications

To develop specimen pooling algorithms that reduce the number of tests needed to test individuals for infectious diseases with multiplex assays.

Genomic Prediction Using Canopy Coverage Image And Genotypic Information In Soybean Via A Hybrid Model, Reka Howard, Diego Jarquin

Department of Statistics: Faculty Publications

Prediction techniques are important in plant breeding as they provide a tool for selection that is more efficient and economical than traditional phenotypic and pedigree based selection. The conventional genomic prediction models include molecular marker information to predict the phenotype. With the development of new phenomics techniques we have the opportunity to collect image data on the plants, and extend the traditional genomic prediction models where we incorporate diverse set of information collected on the plants. In our research, we developed a hybrid matrix model that incorporates molecular marker and canopy coverage information as a weighted linear combination to predict …

Post-Er Stress Biogenesis Of Golgi Is Governed By Giantin, Cole P. Frisbie, Alexander Y. Lushnikov, Alexey V. Krasnoslobodtsev, Jean-Jack Riethoven, Jennifer L. Clarke, Elena I. Stepchenkova, Armen Petrosyan

Department of Statistics: Faculty Publications

Background: The Golgi apparatus undergoes disorganization in response to stress, but it is able to restore compact and perinuclear structure under recovery. This self-organization mechanism is significant for cellular homeostasis, but remains mostly elusive, as does the role of giantin, the largest Golgi matrix dimeric protein. Methods: In HeLa and different prostate cancer cells, we used the model of cellular stress induced by Brefeldin A (BFA). The conformational structure of giantin was assessed by proximity ligation assay and atomic force microscopy. The post-BFA distribution of Golgi resident enzymes was examined by 3D SIM high-resolution microscopy. Results: We detected that giantin …

Recursive Model For Dose-Time Responses In Pharmacological Studies, Saugato Rahman Dhruba, Aminur Rahman, Raziur Rahman, Souparno Ghosh, Ranadip Pal

Department of Statistics: Faculty Publications

Background: Clinical studies often track dose-response curves of subjects over time. One can easily model the dose-response curve at each time point with Hill equation, but such a model fails to capture the temporal evolution of the curves. On the other hand, one can use Gompertz equation to model the temporal behaviors at each dose without capturing the evolution of time curves across dosage

Results: In this article, we propose a parametric model for dose-time responses that follows Gompertz law in time and Hill equation across dose approximately. We derive a recursion relation for dose-response curves over time capturing the …

Comparison Of Green's Functions For A Family Of Boundary Value Problems For Fractional Difference Equations, Paul W. Eloe, Catherine Kublik, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this paper, we obtain sign conditions and comparison theorems for Green's functions of a family of boundary value problems for a Riemann-Liouville type delta fractional difference equation. Moreover, we show that as the length of the domain diverges to infinity, each Green's function converges to a uniquely defined Green's function of a singular boundary value problem.

Step Away From Stepwise, Gary N. Smith

Pomona Economics

Stepwise regression is a popular data-mining tool that uses statistical significance to select the explanatory variables to be used in a multiple-regression model. A fundamental problem with stepwise regression is that some real explanatory variables that have causal effects on the dependent variable may happen to not be statistically significant, while nuisance variables may be coincidentally significant. As a result, the model may fit the data well in-sample, but do poorly out-of-sample. Many Big-Data researchers believe that, the larger the number of possible explanatory variables, the more useful is stepwise regression for selecting explanatory variables. The reality is that stepwise …

Using Neural Networks To Classify Discrete Circular Probability Distributions, Madelyn Gaumer

HMC Senior Theses

Given the rise in the application of neural networks to all sorts of interesting problems, it seems natural to apply them to statistical tests. This senior thesis studies whether neural networks built to classify discrete circular probability distributions can outperform a class of well-known statistical tests for uniformity for discrete circular data that includes the Rayleigh Test¹, the Watson Test², and the Ajne Test³. Each neural network used is relatively small with no more than 3 layers: an input layer taking in discrete data sets on a circle, a hidden layer, and an output …