Statistics and Probability Commons^™

On Generalized Gamma Convolution Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present here characterizations of certain families of generalized gamma convolution distributions of L. Bondesson based on a simple relationship between two truncated moments. We also present a list of well-known random variables whose distributions or the distributions of certain functions of them belong to the class of generalized gamma convolutions.

The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen K. Bansal, Gholamhossein Hamedani, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n) without the assumption of continuity and symmetry for each component X_i:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where all αi≥0 are special weights with ∑i=1nαi=1.

Verifying R Code And Visualizing Power Grid Data: Signature Quality Metrics And Gui Development, Emmanuel C. Herrera, Brett Amidan

STAR Program Research Presentations

Verifying R code and visualizing Power Grid data:

Signature Quality Metrics and GUI development

Author: Emmanuel Herrera

Mentors: Brett Amidan and Landon Sego

There are many bioforensic signatures produced by analytical instruments that are expensive to produce and maintain accuracy. SQM is an R package which will provide subject matter experts with tools that will help them assess the specific quality of signatures and determine their accuracy, utility and cost by simple function calls. Many published academic papers were surveyed on the kinds of metrics already being implemented. Once understood how some metrics measured accuracy, the SQM package was duplicated …

Renal Cryoablation: Investigation Of Periprocedural Visualization To Ols And Treatment Response Quantification, Katherine L. Dextraze

Dissertations and Theses (Open Access)

Cryoablation for small renal tumors has demonstrated sufficient clinical efficacy over the past decade as a non-surgical nephron-sparing approach for treating renal masses for patients who are not surgical candidates. Minimally invasive percutaneous cryoablations have been performed with image guidance from CT, ultrasound, and MRI. During the MRI-guided cryoablation procedure, the interventional radiologist visually compares the iceball size on monitoring images with respect to the original tumor on separate planning images. The comparisons made during the monitoring step are time consuming, inefficient and sometimes lack the precision needed for decision making, requiring the radiologist to make further changes later in …

Objective Bayesian Hypothesis Testing And Estimation For The Risk Ratio In A Correlated 2x2 Table With Structural Zero, Xiaohua Bai

All Theses

We illustrate the construction of an objective Bayesian hypothesis testing and point estimation for the risk ratio in a correlated 2x2 table with structural zero. We solve the problem using Bayesian method through the reference prior, and corresponding posterior distribution of the risk ratio can be derived. Then combined the intrinsic discrepancy, an invariant inforamtion-based loss function, provides an integrated objective Bayesian solution to both hypothesis testing and point estimation problems.

Count Time Series And Discrete Renewal Processes, James Livsey

All Dissertations

Most data collected over time has some degree of periodicity (i.e. seasonally varying
traits). Climate, stock prices, football season, energy consumption, wildlife sightings, and
holiday sales all have cyclical patterns. It should come as no surprise that models that
incorporate periodicity are paramount in the study of time series.
The following work devises time series models for counts (integer-values) that are periodic
and stationary. Foundational work is rst done in constructing a stationary periodic
discrete renewal process (SPDRP). The dynamics of the SPDRP are mathematically interesting
and have many modeling applications, expositions largely unexplored here. This work
develops a SPDRP …

Extreme Value Theory In Periodic Time Series, Zhiyun Gong

All Dissertations

Extreme data points are important in environmental, financial, and insurance settings. In this work, we consider two topics on extremes from environmental data. Many environmental time series have a seasonal structure. The first part presents an approach to identify the rare events of such series based on time series residuals. Here, periodic autoregressive moving-average models are applied to describe the series. The methods justify the application of classical peaks over threshold methods to estimated versions of the one-step-ahead prediction errors of the series. Such methods enable the seasonal means, variances, and autocorrelations of the series to be taken into account. …

Correlates Of Hiv Acquisition In A Cohort Of Black Men Who Have Sex With Men In The United States: Hiv Prevention Trials Network (Hptn) 061, Beryl A. Koblin, Kenneth H. Mayer, Susan H. Eshleman, Lei Wang, Sharon B. Mannheimer, Carlos Del Rio, Steve Shoptaw, Manya Magnus, Susan Buchbinder, Leo Wilton, Ting-Yuan Liu, Vanessa Cummings, Estelle Piwowar-Manning, Sheldon D. Fields, Sam Griffith, Vanessa Elharrar, Darrell Wheeler

Epidemiology Faculty Publications

Background

Black men who have sex with men (MSM) in the United States (US) are affected by HIV at disproportionate rates compared to MSM of other race/ethnicities. Current HIV incidence estimates in this group are needed to appropriately target prevention efforts.

Methods

From July 2009 to October 2010, Black MSM reporting unprotected anal intercourse with a man in the past six months were enrolled and followed for one year in six US cities for a feasibility study of a multi-component intervention to reduce HIV infection. HIV incidence based on HIV seroconversion was calculated as number of events/100 person-years. Multivariate proportional …

Extremal H-Colorings Of Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, a homomorphism from G to H, or H-coloring of G, is a map from the vertices of G to the vertices of H that preserves adjacency. When H is composed of an edge with one looped endvertex, an H-coloring of G corresponds to an independent set in G. Galvin showed that, for sufficiently large n, the complete bipartite graph K_δ,n-δ is the n-vertex graph with minimum degree δ that has the largest number of independent sets.

In this paper, we begin the project of generalizing this …

Testing The Relative Performance Of Data Adaptive Prediction Algorithms: A Generalized Test Of Conditional Risk Differences, Benjamin A. Goldstein, Eric Polley, Farren Briggs, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In statistical medicine comparing the predictability or fit of two models can help to determine whether a set of prognostic variables contains additional information about medical outcomes, or whether one of two different model fits (perhaps based on different algorithms, or different set of variables) should be preferred for clinical use. Clinical medicine has tended to rely on comparisons of clinical metrics like C-statistics and more recently reclassification. Such metrics rely on the outcome being categorical and utilize a specific and often obscure loss function. In classical statistics one can use likelihood ratio tests and information based criterion if the …

Attributing Effects To Interactions, Tyler J. Vanderweele, Eric J. Tchetgen Tchetgen

Harvard University Biostatistics Working Paper Series

A framework is presented which allows an investigator to estimate the portion of the effect of one exposure that is attributable to an interaction with a second exposure. We show that when the two exposures are independent, the total effect of one exposure can be decomposed into a conditional effect of that exposure and a component due to interaction. The decomposition applies on difference or ratio scales. We discuss how the components can be estimated using standard regression models, and how these components can be used to evaluate the proportion of the total effect of the primary exposure attributable to …

The Estimation And Evaluation Of Optimal Thresholds For Two Sequential Testing Strategies, Amber R. Wilk

Theses and Dissertations

Many continuous medical tests often rely on a threshold for diagnosis. There are two sequential testing strategies of interest: Believe the Positive (BP) and Believe the Negative (BN). BP classifies a patient positive if either the first test is greater than a threshold θ1 or negative on the first test and greater than θ2 on the second test. BN classifies a patient positive if the first test is greater than a threshold θ3 and greater than θ4 on the second test. Threshold pairs θ = (θ1, θ2) or (θ3, θ4), depending on strategy, are defined as optimal if they maximized …

Sample Size Considerations In The Design Of Cluster Randomized Trials Of Combination Hiv Prevention, Rui Wang, Ravi Goyal, Quanhong Lei, M. Essex, Victor Degruttola

Harvard University Biostatistics Working Paper Series

No abstract provided.

Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky

Publications and Research

The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional …

Cardiovascular Outcome Trials In Type 2 Diabetes And The Sulphonylurea Controversy: Rationale For The Active-Comparator Carolina Trial, Julio Rosenstock, Nikolaus Marx, Steven E. Kahn, Bernard Zinman, John J. Kastelein, John M. Lachin, Erich Bluhmki, Sanjay Patel, Odd-Erik Johansen, Hans-Jurgen Woerle

Epidemiology Faculty Publications

Sulphonylureas (SUs) are widely used glucose-lowering agents in type 2 diabetes mellitus (T2DM) with apparent declining efficacy over time. Concerns have been raised from observational retrospective studies on the cardiovascular (CV) safety of SUs but there are few long-term data on CV outcomes from randomized controlled trials (RCTs) involving the use of this class of agents. Most of the observational studies and registry data are conflicting and vary with study population and methodology used for analyses. To address the SU controversy, we reviewed the recently published literature (until end of the year 2011) to evaluate the impact of SUs on …

Modelling Locally Changing Variance Structured Time Series Data By Using Breakpoints Bootstrap Filtering, Rajan Lamichhane

Mathematics & Statistics Theses & Dissertations

Stochastic processes have applications in many areas such as oceanography and engineering. Special classes of such processes deal with time series of sparse data. Studies in such cases focus in the analysis, construction and prediction in parametric models. Here, we assume several non-linear time series with additive noise components, and the model fitting is proposed in two stages. The first stage identifies the density using all the clusters information, without specifying any prior knowledge of the underlying distribution function of the time series. The effect of covariates is controlled by fitting the linear regression model with serially correlated errors. In …

Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Toward An Mhealth Intervention For Smoking Cessation, Golam Mushih Tanimul Ahsan, Ivor D. Addo, Sheikh Iqbal Ahamed, Daniel Petereit, Shalini Kanekar, Linda Burhansstipanov, Linda U. Krebs

Mathematics, Statistics and Computer Science Faculty Research and Publications

The prevalence of tobacco dependence in the United States (US) remains alarming. Invariably, smoke-related health problems are the leading preventable causes of death in the US. Research has shown that a culturally tailored cessation counseling program can help reduce smoking and other tobacco usage. In this paper, we present a mobile health (mHealth) solution that leverages the Short Message Service (SMS) or text messaging feature of mobile devices to motivate behavior change among tobacco users. Our approach implements the Theory of Planned Behavior (TPB) and a phase-based framework. We make contributions to improving previous mHealth intervention approaches by delivering personalized …

A Test For Detecting Changes In Closed Networks Based On The Number Of Communications Between Nodes, Christopher S. Wichman

Department of Statistics: Dissertations, Theses, and Student Research

This dissertation presents a formal method for detecting changes in a closed communications network based on an “abnormal” shift in the number of communications between some of the nodes. The method relies on the analyst’s ability to define the network of interest; capture the number of communications between nodes; and to establish a history of normal communications flow between nodes over fixed intervals of time. A metric multi-dimensional scaling technique is then used to represent the network at each time interval with a k-dimensional (k = 1, 2, …) configuration. The affine bi-dimensional regression coefficient of determination (aR²) …

Fast Covariance Estimation For High-Dimensional Functional Data, Luo Xiao, David Ruppert, Vadim Zipunnikov, Ciprian Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

For smoothing covariance functions, we propose two fast algorithms that scale linearly with the number of observations per function. Most available methods and software cannot smooth covariance matrices of dimension J x J with J>500; the recently introduced sandwich smoother is an exception, but it is not adapted to smooth covariance matrices of large dimensions such as J \ge 10,000. Covariance matrices of order J=10,000, and even J=100,000$ are becoming increasingly common, e.g., in 2- and 3-dimensional medical imaging and high-density wearable sensor data. We introduce two new algorithms that can handle very large covariance matrices: 1) FACE: a …