Statistics and Probability Commons^™

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 …

Counting And Coloring Sudoku Graphs, Kyle Oddson

Mathematics and Statistics Dissertations, Theses, and Final Project Papers

A sudoku puzzle is most commonly a 9 × 9 grid of 3 × 3 boxes wherein the puzzle player writes the numbers 1 - 9 with no repetition in any row, column, or box. We generalize the notion of the n² × n² sudoku grid for all n ∈ ℤ^≥2 and codify the empty sudoku board as a graph. In the main section of this paper we prove that sudoku boards and sudoku graphs exist for all such n; we prove the equivalence of [3]'s construction using unions and products of graphs to the definition of …

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 …

Decision-Making In Forensic Identification Tasks, Amanda Luby

Mathematics & Statistics Faculty Works

No abstract provided.

Controlling For Confounding Via Propensity Score Methods Can Result In Biased Estimation Of The Conditional Auc: A Simulation Study, Hadiza I. Galadima, Donna K. Mcclish

Community & Environmental Health Faculty Publications

In the medical literature, there has been an increased interest in evaluating association between exposure and outcomes using nonrandomized observational studies. However, because assignments to exposure are not random in observational studies, comparisons of outcomes between exposed and nonexposed subjects must account for the effect of confounders. Propensity score methods have been widely used to control for confounding, when estimating exposure effect. Previous studies have shown that conditioning on the propensity score results in biased estimation of conditional odds ratio and hazard ratio. However, research is lacking on the performance of propensity score methods for covariate adjustment when estimating the …

Package Development, Jason Klaassen, Randall Pruim

Summer Research

Project MOSAIC maintains several R packages that can be used by any R users. These users can suggest improvements and request new features. In addition, changes to dependency packages and the creation of new packages can require internal changes to the MOSAIC suite of packages. Unit testing is important to make sure that new features work as designed and that updates to packages do not break old behavior.

The main projects I worked on were:

• The mosaic package (updates and unit tests)
• The leaflethex package (new package)
• Lock5WithR Textbook Companion created with bookdown (revise and reformat)

The Dark Sky Character Of Archaeological Landscapes: Cultural Meaning And Conservation Strategies, Frank Prendergast

Book/Book Chapter

This paper presents the first ever study of light pollution at selected Irish prehistoric archaeological landscapes. The concepts of cosmology and landscape are first briefly described and followed by a summary of early human settlement of the island. Building on this, the extant corpus of early prehistoric megalithic burial tombs is illustrated to show their contrasting distribution patterns and typology. Analysis of tomb locations using nearest-neighbour statistical methods reveals evidence of intentional clustering. Further geo-statistical analysis identifies the geographical locations and the density ranking of these nucleated clusters - a feature especially evident in the passage tomb tradition on this …

How Can The Final Goal Of Completely Replacing Animal Procedures Successfully Be Achieved?, Christiane Baumgartl-Simons, Christiane Hohense

Validation of Alternative Methods Collection

Article 23 of European Union (EU) Directive 86/609/EEC required that Member States promote the development and validation of alternative technologies and stated that the European Commission (EC) “shall report before the end of 1987 on the possibility of modifying tests and guidelines” (European Parliament, 1986, Article 23). This Directive was replaced by Directive 2010/63/EU on the protection of animals used for scientific purposes, which now requires that Member States develop and validate alternative approaches much more precisely and specifies that the ultimate objective is the “full replacement of procedures on live animals for scientific and educational purposes, as soon as …