Statistics and Probability Commons^™

From Solute Transport To Chemical Weathering, Allen Hunt, Thomas E. Skinner

Physics Seminars

A theory for conservative solute transport, based on concepts from percolation theory, is applied directly to reactive solute transport. Chemical reactions are assumed to have reached equilibrium at the scale of an individual pore, but at larger length scales, equilibration is limited by solute transport velocities, which are not the same as fluid velocities! The results of this theory already predicted observed dispersivity values for conservative solute transport over ten orders of magnitude of length scale as well as the variation of solute arrival time distributions with medium saturation. We now show that the solute velocity predicts the time-dependence of …

Statistical Methods For Evaluating And Comparing Biomarkers For Patient Treatment Selection, Holly Janes, Marshall D. Brown, Margaret Pepe, Ying Huang

UW Biostatistics Working Paper Series

Despite the heightened interest in developing biomarkers predicting treatment response that are used to optimize patient treatment decisions, there has been relatively little development of statistical methodology to evaluate these markers. There is currently no unified statistical framework for marker evaluation. This paper proposes a suite of descriptive and inferential methods designed to evaluate individual markers and to compare candidate markers. An R software package has been developed which implements these methods. Their utility is illustrated in the breast cancer treatment context, where candidate markers are evaluated for their ability to identify a subset of women who do not benefit …

An Evaluation Of Inferential Procedures For Adaptive Clinical Trial Designs With Pre-Specified Rules For Modifying The Sample Size, Greg P. Levin, Sarah C. Emerson, Scott S. Emerson

UW Biostatistics Working Paper Series

Many papers have introduced adaptive clinical trial methods that allow modifications to the sample size based on interim estimates of treatment effect. There has been extensive commentary on type I error control and efficiency considerations, but little research on estimation after an adaptive hypothesis test. We evaluate the reliability and precision of different inferential procedures in the presence of an adaptive design with pre-specified rules for modifying the sampling plan. We extend group sequential orderings of the outcome space based on the stage at stopping, likelihood ratio test statistic, and sample mean to the adaptive setting in order to compute …

Risk Score Modeling Of Multiple Gene To Gene Interactions Using Aggregated-Multifactor Dimensionality Reduction, Hongying Dai, Richard J. Charnigo, Mara L. Becker, J. Steven Leeder, Alison A. Motsinger-Reif

Statistics Faculty Publications

BACKGROUND: Multifactor Dimensionality Reduction (MDR) has been widely applied to detect gene-gene (GxG) interactions associated with complex diseases. Existing MDR methods summarize disease risk by a dichotomous predisposing model (high-risk/low-risk) from one optimal GxG interaction, which does not take the accumulated effects from multiple GxG interactions into account.

RESULTS: We propose an Aggregated-Multifactor Dimensionality Reduction (A-MDR) method that exhaustively searches for and detects significant GxG interactions to generate an epistasis enriched gene network. An aggregated epistasis enriched risk score, which takes into account multiple GxG interactions simultaneously, replaces the dichotomous predisposing risk variable and provides higher resolution in the quantification …

A Neural Network Model To Translate Brain Developmental Events Across Mammalian Species, Radhakrishnan Nagarajan, Jeffrey N. Jonkman

Biostatistics Faculty Publications

Translating the timing of brain developmental events across mammalian species using suitable models has provided unprecedented insights into neural development and evolution. More importantly, these models can prove to be useful abstractions and predict unknown events across species from known empirical event timing data retrieved from published literature. Such predictions can be especially useful since the distribution of the event timing data is skewed with a majority of events documented only across a few selected species. The present study investigates the choice of single hidden layer feed-forward neural networks (FFNN) for predicting the unknown events from the empirical data. A …

A General Regression Framework For A Secondary Outcome In Case-Control Studies, Eric J. Tchetgen Tchetgen

Harvard University Biostatistics Working Paper Series

No abstract provided.

In Praise Of Simplicity Not Mathematistry! Ten Simple Powerful Ideas For The Statistical Scientist, Roderick J. Little

The University of Michigan Department of Biostatistics Working Paper Series

Ronald Fisher was by all accounts a first-rate mathematician, but he saw himself as a scientist, not a mathematician, and he railed against what George Box called (in his Fisher lecture) "mathematistry". Mathematics is the indispensable foundation for statistics, but our subject is constantly under assault by people who want to turn statistics into a branch of mathematics, making the subject as impenetrable to non-mathematicians as possible. Valuing simplicity, I describe ten simple and powerful ideas that have influenced my thinking about statistics, in my areas of research interest: missing data, causal inference, survey sampling, and statistical modeling in general. …

Catching A Viral Video, T Broxton, Yannet Interian, J Vaver, M Wattenhofer

Master of Science in Analytics (MSAN) Faculty Research

The sharing and re-sharing of videos on social sites, blogs e-mail, and other means has given rise to the phenomenon of viral videos - videos that become popular through internet sharing. In this paper we seek to better understand viral videos on YouTube by analyzing sharing and its relationship to video popularity using millions of YouTube videos. The socialness of a video is quantified by classifying the referrer sources for video views as social (e.g. an emailed link, Facebook referral) or non-social (e.g. a link from related videos). We find that viewership patterns of highly social videos are very different …

Modeling The Impact And Costs Of Semiannual Mass Drug Administration For Accelerated Elimination Of Lymphatic Filariasis, Wilma A. Stolk, Quirine A. Ten Bosch, Sake J. De Vlas, Peter U. Fischer, Gary J. Weil, Ann S. Goldman

Epidemiology Faculty Publications

The Global Program to Eliminate Lymphatic Filariasis (LF) has a target date of 2020. This program is progressing well in many countries. However, progress has been slow in some countries, and others have not yet started their mass drug administration (MDA) programs. Acceleration is needed. We studied how increasing MDA frequency from once to twice per year would affect program duration and costs by using computer simulation modeling and cost projections. We used the LYMFASIM simulation model to estimate how many annual or semiannual MDA rounds would be required to eliminate LF for Indian and West African scenarios with varied …

Environmental Exposure To Pyrethroids And Sperm Sex Chromosome Disomy: A Cross-Sectional Study, Heather A. Young, John D. Meeker, Sheena E. Martenies, Zaida I. Figueroa, Dana Boyd Barr, Melissa J. Perry

Epidemiology Faculty Publications

Background

The role of environmental pesticide exposures, such as pyrethroids, and their relationship to sperm abnormalities are not well understood. This study investigated whether environmental exposure to pyrethroids was associated with altered frequency of sperm sex chromosome disomy in adult men.

Methods

A sample of 75 subjects recruited through a Massachusetts infertility clinic provided urine and semen samples. Individual exposures were measured as urinary concentrations of three pyrethroid metabolites ((3-phenoxybenzoic acid (3PBA), cis- and trans- 3-(2,2-Dichlorovinyl)-1-methylcyclopropane-1,2-dicarboxylic acid (CDCCA and TDCCA)). Multiprobe fluorescence in situ hybridization for chromosomes X, Y, and 18 was used to determine XX, YY, XY, 1818, and …

Modeling, Analysis, And Applications Of Complex Systems, Chuandong Li, Xiaodi Li, Shukai Duan, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

Recent advances in theory and applications of complex dynamical systems have contributed much to the successful handling of certain problems in biology, physics, economics, engineering, and so forth that until recently were thought too difficult to be analyzed. These complex systems may be characterized by systems with uncertainty, impulse, time delay, stochastic perturbation, hybrid dynamics, distributed dynamics, and chaotic dynamics. The overall aim of this special issue is to bring together the latest or innovative knowledge and advances in mathematics for handling complex systems, which may depend largely on methods from mathematical analysis, artificial intelligence, statistics, and engineering, including nonlinear …

A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers, Xiaoming Wang, Jared P. Whitehead

Mathematics and Statistics Faculty Research & Creative Works

An upper bound on the rate of vertical heat transport is established in three dimensions for stress-free velocity boundary conditions on horizontally periodic plates. a variation of the background method is implemented that allows negative values of the quadratic form to yield 'small' (O.1=Pr/) corrections to the subsequent bound. for large (but finite) Prandtl numbers this bound is an improvement over the 'ultimate' Ra1=2 scaling and, in the limit of infinite Pr, agrees with the bound of Ra5=12 recently derived in that limit for stress-free boundaries. © 2013 Cambridge University Press.

Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang, Zhifei Zhang

Mathematics and Statistics Faculty Research & Creative Works

We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. for initial data in Hs, s>d2+1, the existence and uniqueness of solution in C([0,T];Hs) ∪L2(0,T;Hs+2) that is global in time in the two-dimensional case (d=2) and local in time in the three-dimensional case (d=3) are established. Several blow-up criterions in the three-dimensional case are provided as well. One of the tools that we utilized is the Littlewood-Paley theory in order to establish certain key commutator estimates. © 2012 Elsevier Masson SAS.

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.

Consilience: Radiocarbon, Instrumental Neutron Activation Analysis, And Litigation In The Ancestral Caddo Region, Robert Z. Selden Jr.

CRHR: Archaeology

Through the creation and analysis of databases for radiocarbon, instrumental neutron activation analysis (INAA), and law, macro-level trends are exposed that form the framework of a broader research program aimed at advancing ideas of craft specialization and archaeological theory in the ancestral Caddo region of Southwest Arkansas, Northwest Louisiana, Northeast Texas, and Southeast Oklahoma. The findings of this investigation illustrate the research potential that remains buried within the context of cultural resource management (CRM) reports and legal databases (Westlaw and LexisNexis) that is awaiting consumption within regional research designs aimed at exploring the nuances and trends that appear through synthetic …

Visualizing Longitudinal Data With Dropouts, Mithat Gonen

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

A triangle plot is proposed to display longitudinal data with dropouts. The triangle plot is a tool of data visualization that can also serve as a graphical check for informativeness of the dropout process. There are similarities between the lasagna plot and the triangle plot but the explicit use of dropout time as an axis is an advantage of the triangle plot over the more commonly used graphical strategies for longitudinal data. It is possible to interpret the triangle plot as a trellis plot 1 which gives rise to several extensions such as the triangle histogram and the triangle boxplot. …