Statistics and Probability Commons^™

Quantitative Interpretation Of A Genetic Model Of Carcinogenesis Using Computer Simulations, Donghai Dai, Brandon Beck, Xiaofang Wang, Cory Howk, Yi Li

Mathematics and Statistics Faculty Publications

The genetic model of tumorigenesis by Vogelstein et al. (V theory) and the molecular definition of cancer hallmarks by Hanahan and Weinberg (W theory) represent two of the most comprehensive and systemic understandings of cancer. Here, we develop a mathematical model that quantitatively interprets these seminal cancer theories, starting from a set of equations describing the short life cycle of an individual cell in uterine epithelium during tissue regeneration. The process of malignant transformation of an individual cell is followed and the tissue (or tumor) is described as a composite of individual cells in order to quantitatively account for intra-tumor …

Estimating Subject-Specific Treatment Differences For Risk-Benefit Assessment With Competing Risk Event-Time Data, Brian Claggett, Lihui Zhao, Lu Tian, Davide Castagno, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Hierarchical Bayesian Methods For Evaluation Of Traffic Project Efficacy, Andrew Nolan Olsen

Theses and Dissertations

A main objective of Departments of Transportation is to improve the safety of the roadways over which they have jurisdiction. Safety projects, such as cable barriers and raised medians, are utilized to reduce both crash frequency and crash severity. The efficacy of these projects must be evaluated in order to use resources in the best way possible. Five models are proposed for the evaluation of traffic projects: (1) a Bayesian Poisson regression model; (2) a hierarchical Poisson regression model building on model (1) by adding hyperpriors; (3) a similar model correcting for overdispersion; (4) a dynamic linear model; and (5) …

Simple Examples Of Estimating Causal Effects Using Targeted Maximum Likelihood Estimation, Michael Rosenblum, Mark J. Van Der Laan

Johns Hopkins University, Dept. of Biostatistics Working Papers

We present a brief overview of targeted maximum likelihood for estimating the causal effect of a single time point treatment and of a two time point treatment. We focus on simple examples demonstrating how to apply the methodology developed in (van der Laan and Rubin, 2006; Moore and van der Laan, 2007; van der Laan, 2010a,b). We include R code for the single time point case.

Parameter Estimation For The Two-Parameter Weibull Distribution, Mark A. Nielsen

Theses and Dissertations

The Weibull distribution, an extreme value distribution, is frequently used to model survival, reliability, wind speed, and other data. One reason for this is its flexibility; it can mimic various distributions like the exponential or normal. The two-parameter Weibull has a shape (γ) and scale (β) parameter. Parameter estimation has been an ongoing search to find efficient, unbiased, and minimal variance estimators. Through data analysis and simulation studies, the following three methods of estimation will be discussed and compared: maximum likelihood estimation (MLE), method of moments estimation (MME), and median rank regression (MRR). The analysis of wind speed data from …

Utilizing Universal Probability Of Expression Code (Upc) To Identify Disrupted Pathways In Cancer Samples, Michelle Rachel Withers

Theses and Dissertations

Understanding the role of deregulated biological pathways in cancer samples has the potential to improve cancer treatment, making it more effective by selecting treatments that reverse the biological cause of the cancer. One of the challenges with pathway analysis is identifying a deregulated pathway in a given sample. This project develops the Universal Probability of Expression Code (UPC), a profile of a single deregulated biological path- way, and projects it into a cancer cell to determine if it is present. One of the benefits of this method is that rather than use information from a single over-expressed gene, it pro- …

A Note On The Interpretation Of Scale Values In Multidimensional Scaling Growth Analysis, Cody Ding

Education Sciences and Professional Programs Faculty Works

No abstract provided.

Maximal Sensitive Dependence And The Optimal Path To Epidemic Extinction, Eric Forgoston, Simone Bianco, Leah B. Shaw, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that …

Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang

Mathematics Faculty Publications

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global L2 a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.

An Approach To Nearest Neighboring Search For Multi-Dimensional Data, Yong Shi, Li Zhang, Lei Zhu

Faculty Articles

Finding nearest neighbors in large multi-dimensional data has always been one of the research interests in data mining field. In this paper, we present our continuous research on similarity search problems. Previously we have worked on exploring the meaning of K nearest neighbors from a new perspective in PanKNN [20]. It redefines the distances between data points and a given query point Q, efficiently and effectively selecting data points which are closest to Q. It can be applied in various data mining fields. A large amount of real data sets have irrelevant or obstacle information which greatly affects the effectiveness …

Projective-Planar Graphs With No K3,4-Minor, John Maharry, Dan Slilaty

Mathematics and Statistics Faculty Publications

An exact structure is described to classify the projective‐planar graphs that do not contain a K3, 4‐minor.

Characterizing The Arc, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We offer a mathematical logic framework for talking about when a given topological space is characterizable relative to a “class of its peers.” The framework involves a relational alphabet for which there is a natural way of assigning relational structures to spaces in the peer class; and a putative characterization of the given space consists of a set of first-order sentences over that alphabet, all true for the space. The attempted characterization is a success if any peer space satisfying all the sentences is inevitably homeomorphic to the given space.

For example, it has long been known that the arc …

Common Hypercyclic Vectors For The Conjugate Class Of A Hypercyclic Operator, Kit C. Chan, Rebecca Sanders

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense G_δ set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense …

Signal And Noise In Complex-Valued Sense Mr Image Reconstruction, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure …

Semidistributive Inverse Semigroups, Ii, Kyeong Hee Cheong, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The description by Johnston-Thom and the second author of the inverse semigroups S for which the lattice LJ(S) of full inverse subsemigroups of S is join semidistributive is used to describe those for which (a) the lattice L(S) of all inverse subsemigroups or (b) the lattice lo(S) of convex inverse subsemigroups have that property. In contrast with the methods used by the authors to investigate lower semimodularity, the methods are based on decompositions via G_S, the union of the subgroups of the semigroup (which is necessarily cryptic).

Some Problems And Solutions In The Experimental Science Of Technology: The Proper Use And Reporting Of Statistics In Computational Intelligence, With An Experimental Design From Computational Ethnomusicology, Mehmet Vurkaç

Systems Science Friday Noon Seminar Series

Statistics is the meta-science that lends validity and credibility to The Scientific Method. However, as a complex and advanced Science in itself, Statistics is often misunderstood and misused by scientists, engineers, medical and legal professionals and others. In the area of Computational Intelligence (CI), there have been numerous misuses of statistical techniques leading to the publishing of insupportable results, which, in addition to being a problem in itself, has also contributed to a degree of rift between the Statistics/Statistical Learning community and the Machine Learning/Computational Intelligence community. This talk surveys a number of misuses of statistical inference in CI settings, …

Efektivitas Dan Efisiensi Sistem Informasi Keluarga Berencana Di Puskesmas, Aragar Putri, Besral Besral

Kesmas

Efisiensi dan efektivitas sistem informasi keluarga berencana (KB)-kesehatan yang telah disosialisasikan sejak tahun 2007 dibandingkan dengan sistem yang lama belum diketahui. Suatu penelitian survei dilakukan di empat provinsi, yaitu DKI Jakarta, Lampung, Kalimatan Tengah, dan Bali. Di tiap provinsi dipilih dua kabupaten/kota dan pada tiap kabupaten/kota dipilih dua puskesmas (kecamatan) yang sudah menerapkan sistem informasi KB-kesehatan tersebut. Pengumpulan data dilakukan pada bulan Juni-September 2008. Penelitian ini menemukan bahwa efektivitas dan efisiensi sistem informasi KB yang baru cukup baik, 77,8% responden menyatakan lebih efektif atau sangat lebih efektif dan 66,7% responden menyatakan lebih efisien atau sangat lebih efisien dibandingkan dengan sistem …

Bate Curve In Assessment Of Clinical Utility Of Predictive Biomarkers, Xiao-Hua Zhou, Yunbei Ma

UW Biostatistics Working Paper Series

In this paper, for time-to-event data, we propose a new statistical framework for casual inference in evaluating clinical utility of predictive biomarkers and in selecting an optimal treatment for a particular patient. This new casual framework is based on a new concept, called Biomarker Adjusted Treatment Effect (BATE) curve, which can be used to represent the clinical utility of a predictive biomarker and select an optimal treatment for one particular patient. We then propose semi-parametric methods for estimating the BATE curves of biomarkers and establish asymptotic results of the proposed estimators for the BATE curves. We also conduct extensive simulation …

Tmle: An R Package For Targeted Maximum Likelihood Estimation, Susan Gruber, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Targeted maximum likelihood estimation (TMLE) presents an approach for construction of an efficient double-robust semi-parametric substitution estimator of a target feature of the data generating distribution, such as a statistical association measure or a causal effect parameter. tmle is a recently developed R package that implements TMLE for estimation of the effect of a binary treatment at a single point in time on an outcome of interest, controlling for user supplied covariates: the additive treatment effect, the relative risk, the odds ratio. The package allows outcome data with missingness, and experimental units that contribute repeated records of the point-treatment data …

Causal Inference Under Multiple Versions Of Treatment, Tyler J. Vanderweele, Miguel A. Hernan

COBRA Preprint Series

In this article we discuss the no-multiple-versions-of-treatment assumption and extend the potential outcomes framework to accommodate causal inference under violations of this assumption. A variety of examples are discussed in which the assumption may be violated. Identification results are provided for the overall treatment effect and the effect of treatment on the treated when multiple versions of treatment are present and also for the causal effect comparing a version of one treatment to some other version of the same or a different treatment. Further identification and interpretative results are given for cases in which a treatment variable is dichotomized to …