Statistics and Probability Commons^™

A Bayesian Hierarchical Model For Constrained Distributed Lag Functions: Estimating The Time Course Of Hospitalization Associated With Air Pollution Exposure, Roger Peng, Francesca Dominici, Leah J. Welty

Johns Hopkins University, Dept. of Biostatistics Working Papers

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological …

The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. …

Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.

Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

Oscillation and nonoscillation properties of second order Sturm-Liouville dynamic equations on time scales — for example, second order self-adjoint differential equations and second order Sturm-Liouville difference equations — have attracted much interest. Here we consider a given homogeneous equation and a corresponding equation with forcing term. We give new conditions implying that the latter equation inherits the oscillatory behavior of the homogeneous equation. We also give new conditions that introduce oscillation of the inhomogeneous equation while the homogeneous equation is nonoscillatory. Finally, we explain a gap in a result given in the literature for the continuous and the discrete case. …

The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du

Mathematics and Statistics Faculty Research & Creative Works

The dynamic laws of quantized vortex interactions in the Ginzburg-Landau-Schrödinger equation (GLSE) are analytically and numerically studied. A review of the reduced dynamic laws governing the motion of vortex centers in the GLSE is provided. The reduced dynamic laws are solved analytically for some special initial data. By directly simulating the GLSE with an efficient and accurate numerical method proposed recently in [Y. Zhang, W. Bao, and Q. Du, Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation, European J. Appl. Math., to appear], we can qualitatively and quantitatively compare quantized vortex interaction patterns of the GLSE with those from the …

On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.

Changing The Support Of A Spatial Covariate: A Simulation Study, Tisha L. Hooks, Jeffrey F. Pedersen, David B. Marx, Roch E. Gaussoin

Department of Statistics: Faculty Publications

Researchers are increasingly able to capture spatially referenced data on both a response and a covariate more frequently and in more detail. A combination of geostatisical models and analysis of covariance methods may be used to analyze such data. However, very basic questions regarding the effects of using a covariate whose support differs from that of the response variable must be addressed to utilize these methods most efficiently. In this experiment, a simulation study was conducted to assess the following: (i) the gain in efficiency when geostatistical models are used, (ii) the gain in efficiency when analysis of covariance methods …

Is A Basketball Free-Throw Sequence Nonrandom? A Group Exercise For Undergraduate Statistics Students, Stephen C. Adolph

All HMC Faculty Publications and Research

I describe a group exercise that I give to my undergraduate biostatistics class. The exercise involves analyzing a series of 200 consecutive basketball free-throw attempts to determine whether there is any evidence for sequential dependence in the probability of making a free-throw. The students are given the exercise before they have learned the appropriate statistical tests, so that they can come up with ideas on their own. Students spend a full class period working on the problem, with my guidance and hints. In the next class period, we discuss how each student group approached the problem. I then present several …

The Poor Contribution Of Chimpanzee Experiments To Biomedical Progress, Andrew Knight

Experimentation Collection

Biomedical research on captive chimpanzees incurs substantial nonhuman animal welfare, ethical, and financial costs that advocates claim result in substantial advancements in biomedical knowledge. However, demonstrating minimal contribution toward the advancement of biomedical knowledge generally, subsequent papers did not cite 49.5% (47/95), of 95 experiments randomly selected from a population of 749 published worldwide between 1995 and 2004. Only 14.7% (14/95) were cited by 27 papers that abstracts indicated described well-developed methods for combating human diseases. However, detailed examination of these medical papers revealed that in vitro studies, human clinical and epidemiological studies, molecular assays and methods, and genomic studies …

Overcoming Ideology: Why It Is Necessary To Create A Culture In Which The Ethical Review Of Protocols Can Flourish, Bernard E. Rollin

Experimentation Collection

My objective in this commentary is to describe and discuss a major threat to the continued thriving of science in our society, which is all the more insidious because it is largely unrecognized by those in the scientific community who are in a position to rectify the problem. Astute people in that community are well aware of many threats to science that include but are not limited to the following: appalling public scientific illiteracy; the unfortunate resurgence of “magic thinking”—reflected in turn in the reappearance of Creationism, which is hostile to evolution—and the billions of dollars spent on evidentially baseless …

Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider the differentiability of weak solutions of linear parabolic equations with respect to parameters and initial data. under natural assumptions, it is shown that solutions possess as much differentiability with respect to the data as do the terms appearing in the equation. The derivatives are shown to satisfy the appropriate sensitivity equations. The theoretical results are illustrated with an example.

Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques we establish some oscillation criteria for the second order Emden-Fowler dynamic equation on a time scale. Such equations contain the classical Emden-Fowler equation as well as their discrete counterparts. The classical oscillation results of Atkinson (in the superlinear case) and Belohorec (in the sublinear case) are extended in this paper to Emden-Fowler dynamic equations on any time scale.

Boosted Classification Trees And Class Probability/Quantile Estimation, David Mease, A. Wyner, A. Buja

Faculty Publications

The standard by which binary classifiers are usually judged, misclassification error, assumes equal costs of misclassifying the two classes or, equivalently, classifying at the 1/2 quantile of the conditional class probability function P[y = 1jx]. Boosted classification trees are known to perform quite well for such problems. In this article we consider the use of standard, off-the-shelf boosting for two more general problems: 1) classification with unequal costs or, equivalently, classification at quantiles other than 1/2, and 2) estimation of the conditional class probability function P[y = 1jx]. We first examine whether the latter problem, estimation of P[y = 1jx], …

A Robust Measure Of Correlation Between Two Genes On A Microarray, Johanna S. Hardin, Aya Mitani '06, Leanne Hicks, Brian Vankoten

Pomona Faculty Publications and Research

Background

The underlying goal of microarray experiments is to identify gene expression patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions could be co-expressed and show similar patterns of expression on a microarray. Using any of a variety of clustering methods or gene network analyses we can partition genes of interest into groups, clusters, or modules based on measures of similarity. Typically, Pearson correlation is used to measure distance (or similarity) before implementing a clustering algorithm. Pearson correlation is quite susceptible to outliers, however, an unfortunate characteristic when dealing …

Cholecystectomy Deferral In Patients With Endoscopic Sphincterotomy, Vivian Mcalister, Eric Davenport, Elizabeth Renouf

Surgery Publications

BACKGROUND: Cholecystectomy is not required in up to 64% of patients who adopt a wait-and-see policy after endoscopic clearance of common bile duct stones. Although reports of retrospective cohort series have shown a higher mortality among patients who defer cholecystectomy, it is not known if this is due to the patients' premorbid health status or due to the deferral of cholecystectomy. Randomised clinical trials of prophylactic cholecystectomy versus wait-and-see have not had sufficient power to demonstrate differences in survival.

OBJECTIVES: To evaluate the beneficial and harmful effects of cholecystectomy deferral (wait-and-see) versus elective (prophylactic) cholecystectomy in patients who have had …

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-di erential operator with Wentzell boundary conditions.

A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia

Mathematics Faculty Research Publications

We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ₁ of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal control ĝ_α with optimal state u_ĝαα and optimal adjoint state p_ĝαα are convergent as α → 1 …

Acer Conquest Version 2.0: Generalised Item Response Modelling Software, Margaret L. Wu, Ray J. Adams, Mark R. Wilson, Samuel A. Haldane

Measurement and statistics

No abstract provided.

The Extent Of Interaction Between The Scallop And Prawn Fleets In The Shark Bay Scallop Managed Fishery, John Dickson

Theses : Honours

The Shark Bay Managed Scallop Fishery is Western Australia's most important scallop fishery with an annual value of between $2 and $58 million. In addition to this the fishery is an important source of regional employment with approximately 160 skippers and crew employed during the 2005 season. Two separate fleets are permitted to fish for scallops in this fishery, the first consisting of dedicated scallop fishing vessels (Class A licences) and the second of prawn fishing vessels (Class B licences) that are allowed to take scallops under a catch sharing arrangement. Concerns exist over the interactions between these two fleets …

Why De Minimis?, Matthew D. Adler

Faculty Scholarship

De minimis cutoffs are a familiar feature of risk regulation. This includes the quantitative individual risk thresholds for fatality risks employed in many contexts by EPA, FDA, and other agencies, such as the 1-in-1 million lifetime cancer risk cutoff; extreme event cutoffs for addressing natural hazards, such as the 100 - year - flood or 475 - year - earthquake; de minimis failure probabilities for built structures; the exclusion of low - probability causal models; and other policymaking criteria. All these tests have a common structure, as I show in the Article. A de minimis test, broadly defined, tells the …

An Analysis Of Services Provided By Faith-Based Organizations To Cleveland’S Ward 17 Community, Mark Salling

All Maxine Goodman Levin School of Urban Affairs Publications

No abstract provided.

On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.

A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis

Mathematics and Statistics Faculty Publications

Six graphical procedures to check the assumption of proportional hazards for the Cox model are described and compared. A new way of comparing the graphical procedures using a Kolmogorov-Smirnov like maximum deviation criterion for rejection is derived for each procedure. The procedures are evaluated in a simulation study under proportional hazards and five different forms of nonproportional hazards: (1) increasing hazards, (2) decreasing hazards, (3) crossing hazards, (4) diverging hazards, and (5) nonmonotonic hazards. The procedures are compared in the two-sample case corresponding to two groups with different hazard functions. None of the procedures under consideration require partitioning of the …

Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty

Mathematics and Statistics Faculty Publications

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">−K5 and then taking 1-, 2-, and 3-sums with balanced signed grap

A Comparison Of Techniques To Forecast Consumer Satisfaction For Vehicle Ride, Elizabeth A. Cudney, David Drain, Kenneth M. Ragsdell, Kioumars Paryani

Engineering Management and Systems Engineering Faculty Research & Creative Works

This paper presents a comparison of methods for the identification of a reduced set of useful variables using a multidimensional system. the Mahalanobis-Taguchi System and a standard statistical technique are used reduce the dimensionality of vehicle ride based on consumer satisfaction ratings. the Mahalanobis-Taguchi System and cluster analysis are applied to vehicle ride. the research considers 67 vehicle data sets for the 6 vehicle ride parameters. This paper applies the Mahalanobis-Taguchi System to forecast consumer satisfaction and provides a comparison of results with those obtained from a standard statistical approach to the problem. Copyright © 2007 SAE International.

การเปรียบเทียบสถิติเดอร์บินวัตสัน สถิติวอลลิส กับตัวสถิติบูทสแตรปสำหรับการตรวจสอบอัตตสหสัมพันธ์ของความคลาดเคลื่อนในตัวแบบถดถอยเชิงเส้น, กิตติพงษ์ ไตรทิพย์พานิชย์

Chulalongkorn University Theses and Dissertations (Chula ETD)

การวิจัยครั้งนี้ ต้องการศึกษาเปรียบเทียบความสามารถในการควบคุมความคลาดเคลื่อนประเภทที่ 1 และอำนาจการทดสอบของตัวสถิติที่ใช้ตรวจสอบอัตตสหสัมพันธ์ ของความคลาดเคลื่อนในสถานการณ์ดังต่อไปนี้ 1) เปรียบเทียบสถิติ 3 วิธี คือ ตัวสถิติเดอร์บินวัตสัน บูทสแตรปเดอร์บินวัตสัน และ บูทสแตรปโรล ในการตรวจสอบอัตตสหสัมพันธ์ตำแหน่งที่ 1 2) เปรียบเทียบสถิติ 3 วิธี คือ ตัวสถิติวอลลิส บูทสแตรปวอลลิส และบูทสแตรปโรล และในการตรวจสอบอัตตสหสัมพันธ์ตำแหน่งที่ 4 เมื่อจำนวนตัวแปรอิสระเท่ากับ 1, 2 และ 5 และกำหนดขนาดตัวอย่างที่ทำการศึกษา คือ 15, 20, 50, 60, 90 และ 100 สำหรับในแต่ละสถานการณ์ ข้อมูลที่ใช้ในการวิจัยนี้ได้จากการทดลองด้วยเทคนิคมอนติคาร์โล โดยจำลองการทดลองด้วยเครื่องคอมพิวเตอร์ 1000 ครั้ง สำหรับแต่ละสถานการณ์ที่ระดับนัยสำคัญ 0.05 ผลวิจัยสรุปได้ดังนี้ 1. ความสามารถในการควบคุมความคลาดเคลื่อนประเภทที่ 1 เมื่อมีอัตตสหสัมพันธ์ ตำแหน่งที่ 1 ตัวสถิติบูทสแตรปเดอร์บินวัตสัน และ บูทสแตรปโรล สามารถควบคุมความคลาดเคลื่อนประเภทที่ 1 ได้ในทุกกรณี และเมื่อมีอัตตสหสัมพันธ์ ตำแหน่งที่ 4 ตัวสถิติบูทสแตรปวอลลิส และ บูทสแตรปโรล สามารถควบคุมความคลาดเคลื่อนประเภทที่ 1 ได้ในทุกกรณี 2. อำนาจการทดสอบ เมื่อมีอัตตสหสัมพันธ์ ตำแหน่งที่ 1 โดยทั่วไปตัวสถิติบูทสแตรปเดอร์บินวัตสันให้อำนาจการทดสอบสูงที่สุด และเมื่อมีอัตตสหสัมพันธ์ ตำแหน่งที่ 4 ตัวสถิติบูทสแตรปวอลลิส จะให้ค่าอำนาจการทดสอบที่สูงสุด

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn

Mathematics Faculty Publications

We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.

Community Service-Learning In Statistics: Course Design And Assessment, Debra L. Hydorn

Mathematics Articles

Service-learning projects are a useful method for students to learn both the practice and value of statistical methods. Effective service learning, however, depends on several factors and can be implemented according to a variety of models. In this article, different models for incorporating service-learning in statistics courses are presented along with example statistics courses. Principles for good service-learning practice will also be presented as a means for assessing the quality of a service-learning course component.