Statistics and Probability Commons^™

Set It And Forget It: Approximating The Set Once Strip Cover Problem, Amotz Bar-Noy, Benjamin Baumer, Dror Rawitz

Mathematics Sciences: Faculty Publications

We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard and that RoundRobin, the algorithm in which the sensors take turns covering the entire region, has a tight approximation guarantee of 3. Moreover, we …

Concerns About Least Squares Estimation For The Three-Parameter Weibull Distribution: Case Study Of Statistical Software, William V. Harper, Thomas R. James

Mathematics Faculty Scholarship

Least Squares estimation of the 2-parameter Weibull distribution is straightforward; however, there are multiple methods for least squares estimation of the 3-parameter Weibull. The third parameter for the 3-parameter Weibull distribution shifts the origin from 0 to some generally positive value sometimes called the location, threshold, or minimum life. The different methods used by the packages result in fairly major differences in the estimated parameters between the statistical packages. This may have implications for those needing to estimate or apply the results of a 3-parameter Weibull distribution that is used frequently in practice. The results are analyzed in detail based …

Gaise Into The Future: Updating A Landmark Report For An Increasingly Data-Centric World, Michelle Everson, Paul Velleman, Beverly Wood, John Gabrosek, Megan Mocko, Robert Carver

Publications

Ever since its official endorsement by the American Statistical Association in 2005, the Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report has had a profound impact on the teaching of statistics. Now, a decade later, it is important to recognize the changing nature in what and how we teach our introductory statistics students. Changes in technology and assessment practices, just over the past 10 years, have made it possible to do new and exciting things in our courses, in very different ways than were envisioned by the authors of the original GAISE College Report. Further, our world …

Orbital Simulations Of Laser-Propelled Spacecraft, Qicheng Zhang, Kevin J. Walsh, Carl Melis, Gary B. Hughes, Philip M. Lubin

Statistics

Spacecraft accelerate by directing propellant in the opposite direction. In the traditional approach, the propellant is carried on board in the form of material fuel. This approach has the drawback of being limited in Delta v by the amount of fuel launched with the craft, a limit that does not scale well to high Delta v due to the massive nature of the fuel. Directed energy photon propulsion solves this problem by eliminating the need for on-board fuel storage. We discuss our system which uses a phased array of lasers to propel the spacecraft which contributes no mass to the …

Local Phase Control For A Planar Array Of Fiber Laser Amplifiers, Patrick Steffanic, Benjamin T. Johannes, Claudia A. Sison, Gary Hughes, Philip Lubin, Peter Meinhold, Johnathan Suen, Hugh O'Neill, Miikka Kangas, Travis Brashears, Qicheng Zhang, Janelle Griswold, Jordan Riley, Caio Motta

Statistics

Arrays of phase-locked lasers have been developed for numerous directed-energy applications. Phased-array designs are capable of producing higher beam intensity than similar sized multi-beam emitters, and also allow beam steering and beam profile manipulation. In phased-array designs, individual emitter phases must be controllable, based on suitable feedback. Most current control schemes sample individual emitter phases, such as with an array-wide beam splitter, and compare to a master phase reference. Reliance on a global beam splitter limits scalability to larger array sizes due to lack of design modularity. This paper describes a conceptual design and control scheme that relies only on …

Confident Difference Criterion: A New Bayesian Differentially Expressed Gene Selection Algorithm With Applications., Fang Yu, Ming-Hui Chen, Lynn Kuo, Heather Talbott, John S. Davis

Journal Articles: Biostatistics

BACKGROUND: Recently, the Bayesian method becomes more popular for analyzing high dimensional gene expression data as it allows us to borrow information across different genes and provides powerful estimators for evaluating gene expression levels. It is crucial to develop a simple but efficient gene selection algorithm for detecting differentially expressed (DE) genes based on the Bayesian estimators.

RESULTS: In this paper, by extending the two-criterion idea of Chen et al. (Chen M-H, Ibrahim JG, Chi Y-Y. A new class of mixture models for differential gene expression in DNA microarray data. J Stat Plan Inference. 2008;138:387-404), we propose two new gene …

A Framework For Inferring Unobserved Multistrain Epidemic Subpopulations Using Synchronization Dynamics, Eric Forgoston, Leah B. Shaw, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A new method is proposed to infer unobserved epidemic subpopulations by exploiting the synchronization properties of multistrain epidemic models. A model for dengue fever is driven by simulated data from secondary infective populations. Primary infective populations in the driven system synchronize to the correct values from the driver system. Most hospital cases of dengue are secondary infections, so this method provides a way to deduce unobserved primary infection levels. We derive center manifold equations that relate the driven system to the driver system and thus motivate the use of synchronization to predict unobserved primary infectives. Synchronization stability between primary and …

Historical Prediction Modeling Approach For Estimating Long-Term Concentrations Of Pm In Cohort Studies Before The 1999 Implementation Of Widespread Monitoring, Sun-Young Kim, Casey Olives, Lianne Sheppard, Paul D. Sampson, Timothy V. Larson, Joel Kaufman

UW Biostatistics Working Paper Series

Introduction: Recent cohort studies use exposure prediction models to estimate the association between long-term residential concentrations of PM_2.5 and health. Because these prediction models rely on PM_2.5 monitoring data, predictions for times before extensive spatial monitoring present a challenge to understanding long-term exposure effects. The Environmental Protection Agency (EPA) Federal Reference Method (FRM) network for PM_2.5 was established in 1999. We evaluated a novel statistical approach to produce high quality exposure predictions from 1980-2010 for epidemiological applications.

Methods: We developed spatio-temporal prediction models using geographic predictors and annual average PM_2.5 data from 1999 through 2010 from …

Model Selection For Gaussian Mixture Models For Uncertainty Qualification, Yiyi Chen, Guang Lin, Xuan Liu

The Summer Undergraduate Research Fellowship (SURF) Symposium

Clustering is task of assigning the objects into different groups so that the objects are more similar to each other than in other groups. Gaussian Mixture model with Expectation Maximization method is the one of the most general ways to do clustering on large data set. However, this method needs the number of Gaussian mode as input(a cluster) so it could approximate the original data set. Developing a method to automatically determine the number of single distribution model will help to apply this method to more larger context. In the original algorithm, there is a variable represent the weight of …

C-Learning: A New Classification Framework To Estimate Optimal Dynamic Treatment Regimes, Baqun Zhang, Min Zhang

The University of Michigan Department of Biostatistics Working Paper Series

Personalizing treatment to accommodate patient heterogeneity and the evolving nature of a disease over time has received considerable attention lately. A dynamic treatment regime is a set of decision rules, each corresponding to a decision point, that determine that next treatment based on each individual’s own available characteristics and treatment history up to that point. We show that identifying the optimal dynamic treatment regime can be recast as a sequential classification problem and is equivalent to sequentially minimizing a weighted expected misclassification error. This general classification perspective targets the exact goal of optimally individualizing treatments and is new and fundamentally …

On Simple Relations Between Difference-In-Differences And Negative Outcome Control Of Unobserved Confounding, Tamar Sofer, David B. Richardson, Elena Colincino, Joel Schwartz, Eric J. Tchetgen Tchetgen

Harvard University Biostatistics Working Paper Series

No abstract provided.

Lepski's Method And Adaptive Estimation Of Nonlinear Integral Functionals Of Density, Rajarshi Mukherjee, Eric J. Tchetgen Tchetgen, James M. Robins

Harvard University Biostatistics Working Paper Series

No abstract provided.

Directed Energy Interstellar Propulsion Of Wafersats, Travis Brashears, Philip Lubin, Gary B. Hughes, Kyle Mcdonough, Sebastian Arias, Alex Lang, Caio Motta, Peter Meinhold, Payton Batliner, Janelle Griswold, Qicheng Zhang, Yusuf Alnawakhtha, Kenyon Prater, Jonathan Madajian, Olivia Sturman, Jana Gergieva, Aidan Gilkes, Bret Silverstein

Statistics

In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration and shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with the Voyager 1 spacecraft launched in 1977 finally leaving the solar system after 37 years of flight at a speed of 17 km/s or less than 0.006% the speed of light. As remarkable as this is, we will never reach even the nearest stars with our current propulsion technology in even 10 millennium. We have to radically rethink …

Local Phase Control For A Planar Array Of Fiber Laser Amplifiers, Patrick Steffanic, Benjamin T. Johannes, Claudia A. Sison, Gary B. Hughes, Philip Lubin, Peter Meinhold, Johnathan Suen, Hugh O'Neill, Miikka Kangas, Travis Brashears, Qicheng Zhang, Janelle Griswold, Jordan Riley, Caio Motta

Statistics

Arrays of phase-locked lasers have been developed for numerous directed-energy applications. Phased-array designs are capable of producing higher beam intensity than similar sized multi-beam emitters, and also allow beam steering and beam profile manipulation. In phased-array designs, individual emitter phases must be controllable, based on suitable feedback. Most current control schemes sample individual emitter phases, such as with an array-wide beam splitter, and compare to a master phase reference. Reliance on a global beam splitter limits scalability to larger array sizes due to lack of design modularity. This paper describes a conceptual design and control scheme that relies only on …

Stand-Off Molecular Composition Analysis, Gary B. Hughes, Philip Lubin, Peter Meinhold, Hugh O'Neill, Travis Brashears, Qicheng Zhang, Janelle Griswold, Jordan Riley, Caio Motta

Statistics

Composition of distant stars can be explored by observing absorption spectra. Stars produce nearly blackbody radiation that passes through the cloud of vaporized material surrounding the star. Characteristic absorption lines are discernible with a spectrometer, and atomic composition is investigated by comparing spectral observations with known material profiles. Most objects in the solar system—asteroids, comets, planets, moons—are too cold to be interrogated in this manner. Material clouds around cold objects consist primarily of volatiles, so bulk composition cannot be probed. Additionally, low volatile density does not produce discernible absorption lines in the faint signal generated by cold objects. We propose …

Mapping Open Water Bodeis With Optical Remote Sensing, Mary Ellen O'Donnell, Erika Podest

STAR Program Research Presentations

There is interest in mapping open water bodies using remote sensing data. Coverage and persistence of open water is currently a poorly measured variable due to its spatial and temporal variability across landscapes, especially in remote areas. The presence and persistence of open water is one of the primary indicators of conditions suitable for mosquito breeding habitats. Predicting the risk of mosquito caused disease outbreaks is a required step towards their control and eradication. Satellite observations can provide needed data to support agency decisions for deployment of preventative measures and control resources. This study, which will try to map open …

Extended Followup Of A Cohort Of Chromium Production Workers, Herman Jones Gibb, Peter St. John Lees, Jing Wang, Keri O'Leary

Epidemiology Faculty Publications

Background

The current study evaluates the mortality of 2,354 workers first employed at a Baltimore chromate production plant between 1950 and 1974.

Methods

The National Death Index (NDI Plus) was used to determine vital status and cause of death. Cumulative chromium (VI) exposure and nasal and skin irritation were evaluated as risk factors for lung cancer mortality.

Results

There are 91,186 person-years of observation and 217 lung cancer deaths. Cumulative chromium (VI) exposure, nasal irritation, nasal perforation, nasal ulceration, and other forms of irritation (e.g., skin irritation) were associated with lung cancer mortality.

Conclusion

Cumulative chromium (VI) exposure was a …

Directed Energy Deflection Laboratory Measurements, Travis Brashears, Philip Lubin, Gary B. Hughes, Peter Meinhold, Jonathan Suen, Payton Batliner, Caio Motta, Janelle Griswold, Miikka Kangas, Isabella Johansson, Yusuf Alnawakhtha, Kenyon Prater, Alex Lang, Jonathan Madajian

Statistics

We report on laboratory studies of the effectiveness of directed energy planetary defense as a part of the DE-STAR (Directed Energy System for Targeting of Asteroids and exploRation) program. DE-STAR and DE-STARLITE are directed energy "stand-off" and "stand-on" programs, respectively. These systems consist of a modular array of kilowatt-class lasers powered by photovoltaics, and are capable of heating a spot on the surface of an asteroid to the point of vaporization. Mass ejection, as a plume of evaporated material, creates a reactionary thrust capable of diverting the asteroid’s orbit. In a series of papers, we have developed a theoretical basis …

Simulations Of Directed Energy Thrust On Rotating Asteroids, Janelle Griswold, Jonathan Madajian, Isabella Johansson, Krysten Pfau, Philip Lubin, Gary B. Hughes, Aidan Gilkes, Peter Meinhold, Caio Motta, Travis Brashears, Qicheng Zhang

Statistics

Asteroids that threaten Earth could be deflected from their orbits using directed energy to vaporize the surface, as the ejected plume creates a reaction thrust that alters the asteroid’s trajectory. In this situation, a critical issue is the rotation of the asteroid relative to the directed energy beam, as this will reduce the average thrust magnitude and modify the thrust direction. Flux levels required to evaporate surface material depend on the surface material composition, rotation rate, albedo, and thermal and bulk mechanical properties of the asteroid. The observed distribution of asteroid rotation rates is used, along with an estimated range …

Sexual Networks And Hiv Risk Among Black Men Who Have Sex With Men In 6 U.S. Cities, Hong-Van Tieu, Ting-Yuan Liu, Sophia Hussen, Matthew Connor, Lei Wang, Gregory Phillips Ii, + 11 More

Epidemiology Faculty Publications

Background

Sexual networks may place U.S. Black men who have sex with men (MSM) at increased HIV risk.

Methods

Self-reported egocentric sexual network data from the prior six months were collected from 1,349 community-recruited Black MSM in HPTN 061, a multi-component HIV prevention intervention feasibility study. Sexual network composition, size, and density (extent to which members are having sex with one another) were compared by self-reported HIV serostatus and age of the men. GEE models assessed network and other factors associated with having a Black sex partner, having a partner with at least two age category difference (age difference between …

Beta-Binomial Kriging: A New Approach To Modeling Spatially Correlated Proportions, Aimee Schwab

Department of Statistics: Dissertations, Theses, and Student Research

Spatially correlated count data sets appear often in applied data analysis problems, but there is little consensus in the literature about how best to analyze the data. The two prevailing approaches provide accurate parameter estimates and predictions, at the cost of model interpretability and simplicity. This dissertation will present a new approach to modeling spatially correlated binomial observations: beta-binomial kriging. The model proposed here is a modified form of spatial kriging which assumes the data are generated from a correlated beta-binomial distribution. Given this assumption, the spatial parameters and predicted values can be estimated using simple matrix algebra. Beta-binomial kriging …

Germline Mutation Detection In Next Generation Sequencing Data And Tp53 Mutation Carrier Probability Estimation For Li-Fraumeni Syndrome, Gang Peng

Dissertations and Theses (Open Access)

Next generation sequencing technology has been widely used in genomic analysis, but its application has been compromised by the missing true variants, especially when these variants are rare. We proposed a family-based variant calling method, FamSeq, integrating Mendelian transmission information with de novo mutation and sequencing data to improve the variant calling accuracy. We investigated the factors impacting the improvement of family-based variant calling in simulation data and validated it in real sequencing data. In both simulation and real data, FamSeq works better than the single individual based method.

In FamSeq, we implemented four different methods for the Mendelian genetic …

Computational Modeling Of Rna-Small Molecule And Rna-Protein Interactions, Lu Chen

Dissertations and Theses (Open Access)

The past decade has witnessed an era of RNA biology; despite the considerable discoveries nowadays, challenges still remain when one aims to screen RNA-interacting small molecule or RNA-interacting protein. These challenges imply an immediate need for cost-efficient while predictive computational tools capable of generating insightful hypotheses to discover novel RNA-interacting small molecule or RNA-interacting protein. Thus, we implemented novel computational models in this dissertation to predict RNA-ligand interactions (Chapter 1) and RNA-protein interactions (Chapter 2).

Targeting RNA has not garnered comparable interest as protein, and is restricted by lack of computational tools for structure-based drug design. To test the potential …

Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker

Electronic Theses and Dissertations

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …

Robin Chapman On (Her) Mathematics Education, Robin Chapman

Journal of Humanistic Mathematics

No abstract provided.

Long-Time Dynamics Of 2d Double-Diffusive Convection: Analysis And/Of Numerics, Florentina Tone, Xiaoming Wang, Djoko Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. as a consequence, the convergence of the attractors and longtime statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.

Quantifying Measurement Error In Digital Instruments, William B. Laing Iii, Sean Bryant

Faculty Works

A first lab experiment clearly illustrates that a glucose meter is actually an excellent source of both random and systematic error, much to the surprise to students and physicians alike. A histogram is constructed and the utility of the standard deviation and standard error to quantify the uncertainty in each measurement and in the mean value, respectively, is demonstrated. From the first lab on, students are challenged to express and interpret confidence intervals in order to form quantitative conclusions. Assessments reveal that many students find this to be surprisingly challenging.

Computerizing Efficient Estimation Of A Pathwise Differentiable Target Parameter, Mark J. Van Der Laan, Marco Carone, Alexander R. Luedtke

U.C. Berkeley Division of Biostatistics Working Paper Series

Frangakis et al. (2015) proposed a numerical method for computing the efficient influence function of a parameter in a nonparametric model at a specified distribution and observation (provided such an influence function exists). Their approach is based on the assumption that the efficient influence function is given by the directional derivative of the target parameter mapping in the direction of a perturbation of the data distribution defined as the convex line from the data distribution to a pointmass at the observation. In our discussion paper Luedtke et al. (2015) we propose a regularization of this procedure and establish the validity …

What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

For the iterated Prisoner's Dilemma there exist good strategies which solve the problem when we restrict attention to the long-term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent's payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long-term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from …

Caffeine Consumption Contributes To Skin Intrinsic Fluorescence In Type 1 Diabetes., Karen M Eny, Trevor J Orchard, Rachel Grace Miller, John Maynard, Denis M Grant, Tina Costacou, Patricia A. Cleary, Barbara H Braffett, Andrew D Paterson, Dcct/Edic Research Group

GW Biostatistics Center

Background: A variant (rs1495741) in the gene for the N-acetyltransferase 2 (NAT2) protein is associated with skin intrinsic fluorescence (SIF), a noninvasive measure of advanced glycation end products and other fluorophores in the skin. Because NAT2 is involved in caffeine metabolism, we aimed to determine whether caffeine consumption is associated with SIF and whether rs1495741 is associated with SIF independently of caffeine.

Materials and Methods: SIF was measured in 1,181 participants with type 1 diabetes from the Epidemiology of Diabetes Interventions and Complications study. Two measures of SIF were used: SIF1, using a 375-nm excitation light-emitting diode (LED), and …