Applied Statistics Commons^™

A Method For Simulating Burr Type Iii And Type Xii Distributions Through L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate L-moments and the L-correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that L-moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also …

New Tools For Quantitative Decision Analysis In Applied Ecology And Conservation, Adam W. Schapaugh

School of Natural Resources: Dissertations, Theses, and Student Research

Scientists have generated a massive body of theory aimed at predicting and managing the impacts of anthropogenic activities on populations, species, and ecosystems. Transforming this research into knowledge that informs complex decision-making problems remains a major challenge in environmental management and conservation. My dissertation research aims to address this issue through the development and application of mathematical and statistical models. I integrate tools, concepts, and techniques from ecology, applied mathematics, computer science, and statistics to build structured decision-making frameworks for spatial prioritization, resource allocation, and optimal scheduling. I also tackle several of the technical challenges limiting the utility of such …

A Bayesian Regression Tree Approach To Identify The Effect Of Nanoparticles Properties On Toxicity Profiles, Cecile Low-Kam, Haiyuan Zhang, Zhaoxia Ji, Tian Xia, Jeffrey I. Zinc, Andre Nel, Donatello Telesca

COBRA Preprint Series

We introduce a Bayesian multiple regression tree model to characterize relationships between physico-chemical properties of nanoparticles and their in-vitro toxicity over multiple doses and times of exposure. Unlike conventional models that rely on data summaries, our model solves the low sample size issue and avoids arbitrary loss of information by combining all measurements from a general exposure experiment across doses, times of exposure, and replicates. The proposed technique integrates Bayesian trees for modeling threshold effects and interactions, and penalized B-splines for dose and time-response surfaces smoothing. The resulting posterior distribution is sampled via a Markov Chain Monte Carlo algorithm. This …

A Study Of The Effects Of Using Computer Spreadsheets On Student Development Of Algebraic Thinking To Compare Function Growth, Beth Stone

Culminating Projects in Applied Statistics

Problem:

The purpose of this research was to explore the effects of incorporating computer spreadsheets on the development of algebraic thinking as it pertains to growth patterns of functions. The study also examined students' ability to transfer skills learned on a computer spreadsheet to problems using pencil and paper, as well the effect of incorporating computer spreadsheets on student motivation, engagement, and communication. Specific questions addressed in the study include: How does investigating an algebra problem about growth patterns by entering numbers, creating formulas, and noticing patterns on a computer spreadsheet affect students' ability to learn the concepts of linear …

Missing At Random And Ignorability For Inferences About Subsets Of Parameters With Missing Data, Roderick J. Little, Sahar Zanganeh

The University of Michigan Department of Biostatistics Working Paper Series

For likelihood-based inferences from data with missing values, Rubin (1976) showed that the missing data mechanism can be ignored when (a) the missing data are missing at random (MAR), in the sense that missingness does not depend on the missing values after conditioning on the observed data, and (b) the parameters of the data model and the missing-data mechanism are distinct; that is, there are no a priori ties, via parameter space restrictions or prior distributions, between the parameters of the data model and the parameters of the model for the mechanism. Rubin described (a) and (b) as the "weakest …

Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein bottle. We give the full list of 20 excluded minors for the smallest class and make a conjecture about the largest class.

Global Quantitative Assessment Of The Colorectal Polyp Burden In Familial Adenomatous Polyposis Using A Web-Based Tool, Patrick M. Lynch, Jeffrey S. Morris, William A. Ross, Miguel A. Rodriguez-Bigas, Juan Posadas, Rossa Khalaf, Diane M. Weber, Valerie O. Sepeda, Bernard Levin, Imad Shureiqi

Jeffrey S. Morris

Background: Accurate measures of the total polyp burden in familial adenomatous polyposis (FAP) are lacking. Current assessment tools include polyp quantitation in limited-field photographs and qualitative total colorectal polyp burden by video.

Objective: To develop global quantitative tools of the FAP colorectal adenoma burden.

Design: A single-arm, phase II trial.

Patients: Twenty-seven patients with FAP.

Intervention: Treatment with celecoxib for 6 months, with before-treatment and after-treatment videos posted to an intranet with an interactive site for scoring.

Main Outcome Measurements: Global adenoma counts and sizes (grouped into categories: less than 2 mm, 2-4 mm, and greater than 4 mm) were …

Investigation Of A Pregnancy Lifestyle Intervention Using Mediation Analysis And A Power Analysis Simulation, Kelsey Grantham

Statistics

No abstract provided.

Patron-Driven Acquisition And Circulation At An Academic Library: Interaction Effects And Circulation Performance Of Print Books Acquired Via Librarians’ Orders, Approval Plans, And Patrons’ Interlibrary Loan Requests, David C. Tyler, Christina D. Falci, Joyce C. Melvin, Marylou Epp, Anita M. Kreps

UNL Libraries: Faculty Publications

Numerous publications on patron-driven acquisition (PDA) for print books and similar materials have reported that patron-requested materials circulate more. Tying circulation to selector may be failing to address the complex of factors that contributes to items’ circulation. In the present study, the authors revisit a PDA program’s data and to determine whether PDA print books’ circulation advantage persists when the potential interactions of several additional variables are taken into account. As with prior studies, library patrons were significantly better predictors of circulation than were librarians or approval plans. However, librarians proved to be significantly better predictors than were approval plans.

Connecting Big Data With Big Decisions: Ideas For Synthesizing Analytics And Decision Analysis, Jeffrey Keisler

Management Science and Information Systems Faculty Publication Series

This paper describes an approach to connect decision analysis models with outputs of analytic methods applied to various types of big data. Decision analysis models focus on issues of concern to a decision maker and incorporate use of a range of methods and axioms to develop insights about what the decision maker should do. In particular, decision analysis models typically use subjective judgments from the decision maker to describe beliefs about the likelihood of events and the desirability of outcomes. In order for human judgments to be improved by the availability of large amounts of data and processing power, it …

Synthesis: What We Have Learned From The East Texas Radiocarbon Database, Robert Z. Selden Jr., Timothy K. Perttula

CRHR: Archaeology

This poster provides a short overview of what we have learned from the East Texas Radiocarbon Database since it became available on the Council of Texas Archeologists’ website in 2011. These successes are numerous and include the advancement of novel methodological approaches; an improvement in our comprehension of the temporal nuances within the East Texas Archaic; the division of the East Texas Woodland period into Early, Middle and Late; the refinement of Caddo temporal chronology – particularly from a geographic perspective -- and it has provided one line of evidence to use to argue for the fluorescence of corn-based agriculture …

Ceramic Petrofacies: Modeling The Angelina River Basin In East Texas, Robert Z. Selden Jr.

CRHR: Archaeology

Ceramic provenance studies remain the basis of worldwide archaeological research concerned with reconstructing exchange networks, tracing migrations, and informing upon ceramic economy. Unfortunately, Texas archaeologists have been plagued with an inability to trace ceramic production sources to the same extent as researchers within other regions. Ceramic petrofacies models have been employed successfully in archaeological contexts at the San Pedro Valley, Tonto basin, Tucson basin, Agua Fria, and Gila and Phoenix basins in Arizona, but have not yet been employed east of Arizona. Data resulting from the construction of an actualistic petrofacies model in the prehistoric coastal environment of East Texas …

Epistemology And Synthesis: Instrumental Neutron Activation Analysis And The Caddo Tradition, Robert Z. Selden Jr.

CRHR: Archaeology

The statistical groupings illustrated herein represent the current iteration of Caddo INAA compositional groups based upon the chemical composition of archaeologically-recovered ceramics. For some time, a number of Caddo archaeologists have thought these results to be lacking. This poster symbolizes the first step toward a new interpretation of chemical composition groups, and the initial instancce within which GIS has been employed as an analytical tool.

Spatial Dynamics Of U.S. Cultural Resource Law, Robert Z. Selden Jr., C. Britt Bousman

CRHR: Archaeology

The American Antiquities Act, Historic Sites Act, Archeological and Historic Preservation Act, National Historic Preservation Act, American Indian Religious Freedom Act, Archeological Resources Protection Act, Abandoned Shipwreck Act, and the Native American Graves Protection and Repatriation Act comprise the basis of our exploration of cultural resource legislation in the United States. Since the passage of the American Antiquities Act in 1906, 1086 cases have challenged these statutes in U.S. courts. We investigate temporal and regional patterns of the case law to establish whether these laws are uniformly prosecuted throughout the U.S. Our findings suggest that case law is complex and …

Radiocarbon Trends And The East Texas Caddo Tradition (Ca. A.D. 800-1680), Robert Z. Selden Jr., Timothy K. Perttula

CRHR: Archaeology

Through the employment of radiocarbon (¹⁴C) dates as data, we use the date combination process to refine site-specific summed probability distributions for 555 dates from Caddo sites (n = 19) in East Texas with 10 or more ¹⁴C dates. Summed probability distributions are then contrasted across river basins and natural regions with the remainder of the East Texas Caddo Radiocarbon Database (n = 338 dates from 132 other Caddo sites), highlighting the temporal and spatial character of Caddo archaeological sites throughout East Texas.

Improving The Retrieval Of Water Inherent Optical Properties In Noisy Hyperspectral Data Through Statistical Modeling, David B. Gillis, Jeffrey H. Bowles, Wesley J. Moses

Wesley Moses

The use of the Mahalanobis distance in a lookup table approach to retrieval of in-water Inherent Optical Properties (IOPs) led to significant improvements in the accuracy of the retrieved IOPs, as high as 50% in some cases, with an average improvement of 20% over a wide range of case II waters. Previous studies have shown that inherent noise in hyperspectral data can cause significant errors in the retrieved IOPs. For LUT-based retrievals that rely on spectrum matching, the particular metric used for spectral comparisons has a significant effect on the accuracy of the results, especially in the presence of noise …

Sas Macro: Kappa Statistic For Clustered Matched-Pair Data, Zhao Yang

Zhao (Tony) Yang, Ph.D.

The SAS macro was developed to calculate the kappa statistic for the clustered matched-pair data.

Bayesian Inferences For Beta Semiparametric Mixed Models To Analyze Longitudinal Neuroimaging Data, Xiaofeng Wang, Yingxing Li

Xiaofeng Wang

Diffusion tensor imaging (DTI) is a quantitative magnetic resonance imaging technique that measures the three-dimensional diffusion of water molecules within tissue through the application of multiple diffusion gradients. This technique is rapidly increasing in popularity for studying white matter properties and structural connectivity in the living human brain. The major measure derived from the DTI process is known as fractional anisotropy, a continuous measure restricted on the interval (0,1). Motivated from a DTI study of multiple sclerosis, we use a beta semiparametric mixed-effect regression model for the longitudinal neuroimaging data. This work extends the generalized additive model methodology with beta …

Bayesian Nonparametric Regression And Density Estimation Using Integrated Nested Laplace Approximations, Xiaofeng Wang

Xiaofeng Wang

Integrated nested Laplace approximations (INLA) are a recently proposed approximate Bayesian approach to fit structured additive regression models with latent Gaussian field. INLA method, as an alternative to Markov chain Monte Carlo techniques, provides accurate approximations to estimate posterior marginals and avoid time-consuming sampling. We show here that two classical nonparametric smoothing problems, nonparametric regression and density estimation, can be achieved using INLA. Simulated examples and \texttt{R} functions are demonstrated to illustrate the use of the methods. Some discussions on potential applications of INLA are made in the paper.

Using Methods From The Data-Mining And Machine-Learning Literature For Disease Classification And Prediction: A Case Study Examining Classification Of Heart Failure Subtypes, Peter C. Austin

Peter Austin

OBJECTIVE: Physicians classify patients into those with or without a specific disease. Furthermore, there is often interest in classifying patients according to disease etiology or subtype. Classification trees are frequently used to classify patients according to the presence or absence of a disease. However, classification trees can suffer from limited accuracy. In the data-mining and machine-learning literature, alternate classification schemes have been developed. These include bootstrap aggregation (bagging), boosting, random forests, and support vector machines.

STUDY DESIGN AND SETTING: We compared the performance of these classification methods with that of conventional classification trees to classify patients with heart failure (HF) …