Statistics and Probability Commons^™

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. …

On The Simulation Of Longitudinal Discrete Data With Specified Marginal Means And First-Order Antedependence, Matthew Guerra, Justine Shults

UPenn Biostatistics Working Papers

We propose a straightforward approach for simulation of discrete random variables with overdispersion, specified marginal means, and product correlations that are plausible for longitudinal data with equal, or unequal, temporal spacings. The method stems from results we prove for variables with first-order antedependence and linearity of the conditional expectations. The proposed approach will be especially useful for assessment of methods such as generalized estimating equations, which specify separate models for the marginal means and correlation structure of measurements on a subject.

Mixtures Of Receiver Operating Characteristic Curves, Mithat Gonen

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

Rationale and Objectives: ROC curves are ubiquitous in the analysis of imaging metrics as markers of both diagnosis and prognosis. While empirical estimation of ROC curves remains the most popular method, there are several reasons to consider smooth estimates based on a parametric model.

Materials and Methods: A mixture model is considered for modeling the distribution of the marker in the diseased population motivated by the biological observation that there is more heterogeneity in the diseased population than there is in the normal one. It is shown that this model results in an analytically tractable ROC curve which is itself …

The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman

Mathematics Faculty Publications

The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …

A Superposed Log-Linear Failure Intensity Model For Repairable Artillery Systems, Byeong Min Mun, Suk Joo Bae, Paul Kvam

Department of Math & Statistics Faculty Publications

This article investigates complex repairable artillery systems that include several failure modes. We derive a superposed process based on a mixture of nonhomogeneous Poisson processes in a minimal repair model. This allows for a bathtub-shaped failure intensity that models artillery data better than currently used methods. The method of maximum likelihood is used to estimate model parameters and construct confidence intervals for the cumulative intensity of the superposed process. Finally, we propose an optimal maintenance policy for repairable systems with bathtub-shaped intensity and apply it to the artillery-failure data.

Gulf-Wide Decreases In The Size Of Large Coastal Sharks Documented By Generations Of Fishermen, Sean P. Powers, F. Joel Frodrie, Steven B. Scyphers, J. Marcus Drymon, Robert L. Shipp, Gregory W. Stunz

University Faculty and Staff Publications

Large sharks are top predators in most coastal and marine ecosystems throughout the world, and evidence of their reduced prominence in marine ecosystems has been a serious concern for fisheries and ecosystem management. Unfortunately, quantitative data to document the extent, timing, and consequences of changes in shark populations are scarce, thwarting examination of long-term (decadal, century) trends, and reconstructions based on incomplete data sets have been the subject of debate. Absence of quantitative descriptors of past ecological conditions is a generic problem facing many fields of science but is particularly troublesome for fisheries scientists who must develop specific targets for …

The Beverton–Holt Q-Difference Equation, Martin Bohner, Rotchana Chieochan

Mathematics and Statistics Faculty Research & Creative Works

The Beverton–Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton–Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton–Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing–Henson conjectures. © 2013 The Author(s). Published by Taylor & Francis.

Drosophila Melanogaster Selection For Survival After Infection With Bacillus Cereus Spores: Evolutionary Genetic And Phenotypic Investigations Of Respiration And Movement, Junjie Ma, Andrew K. Benson, Stephen D. Kachman, Deidra J. Jacobsen, Lawrence G. Harshman

Department of Statistics: Faculty Publications

Laboratory populations of D.melanogaster have been subjected to selection for survival after live spores of B. cereus were introduced as a pathogenic agent. The present study was designed to investigate correlated traits: respiration as ametabolic trait and movement as a behavioral trait.An underlying hypothesiswas that the evolution of increased survival after B. cereus infection exerts ametabolic cost associated with elevated immunity and this would be detected by increased respiration rates. There was support for this hypothesis in the male response to selection, but not for selected-line females. Two phenotypic effects were also observed in the study. Females especially showed a …

The Change In Differing Leukocyte Populations During Vaccination To Bovine Respiratory Disease And Their Correlations With Lung Scores, Health Records, And Average Daily Gain, R. J. Leach, C. G. Chitko-Mckown, G. L. Bennett, S. A. Jones, Stephen D. Kachman, J. W. Keele, K. A. Leymaster, R. M. Thallman, L. A. Kuehn

Department of Statistics: Faculty Publications

Bovine respiratory disease (BRD) is the most economically important disease in U.S. feedlots. Infection can result in morbidity, mortality, and reduced average daily gain. Cheap and reliable genetic methods of prediction and protection from BRD would be highly advantageous to the industry. The immune response may correlate with BRD incidence. Cattle (n = 2,182) were vaccinated against common viral and bacterial pathogens of BRD. Two blood samples were collected, one during booster vaccination and one 21d later, enabling 3 phenotypes for each trait [prebooster (pre), postbooster (post), and delta (post minus pre)]. From the blood samples innate and adaptive responses …

Prediction In M-Complete Problems With Limited Sample Size, Jennifer Lynn Clarke, Bertrand Clarke, Chi-Wai Yu

Department of Statistics: Faculty Publications

We define a new Bayesian predictor called the posterior weighted median (PWM) and compare its performance to several other predictors including the Bayes model average under squared error loss, the Barbieri-Berger median model predictor, the stacking predictor, and the model average predictor based on Akaike's information criterion. We argue that PWM generally gives better performance than other predictors over a range of M-complete problems. This range is between the M-closed-M-complete boundary and the M-complete- M-open boundary. Indeed, as a problem gets closer to M-open, it seems that M-complete predictive methods begin to break down. Our comparisons rest on extensive simulations …

Predictors Of The Number Of Under-Five Malnourished Children In Bangladesh: Application Of The Generalized Poisson Regression Model, Mohammad Mafijul Islam, Morshed Alam, Md Tariquzaman, Mohammad Alamgir Kabir, Rokhsona Pervin, Munni Begum, Md Mobarak Hossain Khan

Journal Articles: Biostatistics

BACKGROUND: Malnutrition is one of the principal causes of child mortality in developing countries including Bangladesh. According to our knowledge, most of the available studies, that addressed the issue of malnutrition among under-five children, considered the categorical (dichotomous/polychotomous) outcome variables and applied logistic regression (binary/multinomial) to find their predictors. In this study malnutrition variable (i.e. outcome) is defined as the number of under-five malnourished children in a family, which is a non-negative count variable. The purposes of the study are (i) to demonstrate the applicability of the generalized Poisson regression (GPR) model as an alternative of other statistical methods and …

Multiscale Analysis Of Factors That Affect The Distribution Of Sharks Throughout The Northern Gulf Of Mexico, J. Marcus Drymon, Laure Carassou, Sean P. Powers, Mark Grace, John Dindo, Brian Dzwonkowski

University Faculty and Staff Publications

Identification of the spatial scale at which marine communities are organized is critical to proper management, yet this is particularly difficult to determine for highly migratory species like sharks. We used shark catch data collected during 2006–09 from fishery- independent bottom-longline surveys, as well as biotic and abiotic explanatory data to identify the factors that affect the distribution of coastal sharks at 2 spatial scales in the northern Gulf of Mexico. Centered principal component analyses (PCAs) were used to visualize the patterns that characterize shark distributions at small (Alabama and Mississippi coast) and large (northern Gulf of Mexico) spatial scales. …

Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene

Publications and Research

In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.

Food For Thought … Mechanistic Validation, Thomas Hartung, Sebastian Hoffman, Martin Stephens

Experimentation Collection

Validation of new approaches in regulatory toxicology is commonly defined as the independent assessment of the reproducibility and relevance (the scientific basis and predictive capacity) of a test for a particular purpose. In large ring trials, the emphasis to date has been mainly on reproducibility and predictive capacity (comparison to the traditional test) with less attention given to the scientific or mechanistic basis. Assessing predictive capacity is difficult for novel approaches (which are based on mechanism), such as pathways of toxicity or the complex networks within the organism (systems toxicology). This is highly relevant for implementing Toxicology for the 21st …

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

Statistics

No abstract provided.

A Frailty Approach For Survival Analysis With Error-Prone Covariate, Sehee Kim, Yi Li, Donna Spiegelman

The University of Michigan Department of Biostatistics Working Paper Series

This paper discovers an inherent relationship between the survival model with covariate measurement error and the frailty model. The discovery motivates our using a frailty-based estimating equation to draw inference for the proportional hazards model with error-prone covariates. Our established framework accommodates general distributional structures for the error-prone covariates, not restricted to a linear additive measurement error model or Gaussian measurement error. When the conditional distribution of the frailty given the surrogate is unknown, it is estimated through a semiparametric copula function. The proposed copula-based approach enables us to fit flexible measurement error models without the curse of dimensionality as …