Digital Commons Network^™

Fixed-Width Output Analysis For Markov Chain Monte Carlo, Galin L. Jones, Murali Haran, Brian S. Caffo, Ronald Neath

Johns Hopkins University, Dept. of Biostatistics Working Papers

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we …

Designs In Partially Controlled Studies: Messages From A Review, Fan Li, Constantine E. Frangakis

Johns Hopkins University, Dept. of Biostatistics Working Papers

The ability to evaluate effects of factors on outcomes is increasingly important for a class of studies that control some but not all of the factors. Although important advances have been made in methods of analysis for such partially controlled studies,work on designs for such studies has been relatively limited. To help understand why, we review main designs that have been used for such partially controlled studies. Based on the review, we give two complementary reasons that explain the limited work on such designs, and suggest a new direction in this area.

Variable Selection For 1d Regression Models, David J. Olive, Douglas M. Hawkins

Articles and Preprints

Variable selection, the search for j relevant predictor variables from a group of p candidates, is a standard problem in regression analysis. The class of 1D regression models is a broad class that includes generalized linear models. We show that existing variable selection algorithms, originally meant for multiple linear regression and based on ordinary least squares and Mallows’ C_p, can also be used for 1D models. Graphical aids for variable selection are also provided.

2d Quantitative Structure Activity Relationship Modeling Of Methylphenidate Analogues Using Algorithm And Partial Least Square Regression, Noureen Wadhwaniya

Theses

Quantitative Structure-Activity Relationship (QSAR) analysis attempts to develop a predictive model of biological activity based on molecular descriptors. 2D QSAR uses descriptors, such as topological indices, that are independent of molecular conformation. A genetic algorithm - partial least squares (GA-PLS) approach was used to identify the molecular descriptors that correlate to the biological activity (binding affinity) of a set of 80 methylphenidate analogues and to construct a predictive model. The GA code was implemented using the fitness function (1-(n-1)(1-q²)/ (n - c)), where n is the number of compounds, c is the optimal number of components, and q …

The Clustering Of Regression Models Method With Applications In Gene Expression Data, Li-Xuan Qin, Steven G. Self

UW Biostatistics Working Paper Series

Identification of differentially expressed genes and clustering of genes are two important and complementary objectives addressed with gene expression data. For the differential expression question, many "per-gene" analytic methods have been proposed. These methods can generally be characterized as using a regression function to independently model the observations for each gene; various adjustments for multiplicity are then used to interpret the statistical significance of these per-gene regression models over the collection of genes analyzed. Motivated by this common structure of per-gene models, we propose a new model-based clustering method -- the clustering of regression models method, which groups genes that …

Insights Into Latent Class Analysis, Margaret S. Pepe, Holly Janes

UW Biostatistics Working Paper Series

Latent class analysis is a popular statistical technique for estimating disease prevalence and test sensitivity and specificity. It is used when a gold standard assessment of disease is not available but results of multiple imperfect tests are. We derive analytic expressions for the parameter estimates in terms of the raw data, under the conditional independence assumption. These expressions indicate explicitly how observed two- and three-way associations between test results are used to infer disease prevalence and test operating characteristics. Although reasonable if the conditional independence model holds, the estimators have no basis when it fails. We therefore caution against using …

Standardizing Markers To Evaluate And Compare Their Performances, Margaret S. Pepe, Gary M. Longton

UW Biostatistics Working Paper Series

Introduction: Markers that purport to distinguish subjects with a condition from those without a condition must be evaluated rigorously for their classification accuracy. A single approach to statistically evaluating and comparing markers is not yet established.

Methods: We suggest a standardization that uses the marker distribution in unaffected subjects as a reference. For an affected subject with marker value Y, the standardized placement value is the proportion of unaffected subjects with marker values that exceed Y.

Results: We apply the standardization to two illustrative datasets. In patients with pancreatic cancer placement values calculated for the CA 19-9 marker are smaller …

Combining Predictors For Classification Using The Area Under The Roc Curve, Margaret S. Pepe, Tianxi Cai, Zheng Zhang, Gary M. Longton

UW Biostatistics Working Paper Series

No single biomarker for cancer is considered adequately sensitive and specific for cancer screening. It is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification. Typically the objective function that is optimized for combining markers is the likelihood function. In this paper we consider an alternative objective function -- the area under the empirical receiver operating characteristic curve (AUC). We note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function. Like logistic regression it yields …

Cluster Analysis Of Genomic Data With Applications In R, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper, we provide an overview of existing partitioning and hierarchical clustering algorithms in R. We discuss statistical issues and methods in choosing the number of clusters, the choice of clustering algorithm, and the choice of dissimilarity matrix. In particular, we illustrate how the bootstrap can be employed as a statistical method in cluster analysis to establish the reproducibility of the clusters and the overall variability of the followed procedure. We also show how to visualize a clustering result by plotting ordered dissimilarity matrices in R. We present a new R package, hopach, which implements the hybrid clustering method, …

Multiple Testing Procedures And Applications To Genomics, Merrill D. Birkner, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

This chapter proposes widely applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics (Dudoit and van der Laan, 2005; Dudoit et al., 2004a,b; van der Laan et al., 2004a,b; Pollard and van der Laan, 2004; Pollard et al., 2005). Procedures are provided to control Type I error rates defined as tail probabilities for arbitrary functions of the numbers of Type I errors, V_n, and rejected hypotheses, R_n. These error rates include: …

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models, Larry Leon, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are …

A Platform-Independent Software Suite For Statistical Analysis Of High Dimensional Biology Data, David B. Allison, Jacob P. L. Brand, Jode W. Edwards, Gary L. Gadbury, Kyoungmi Kim, Tapan Mehta, Grier P. Page, Amit Patki, Vinodh Srinivasasainagendra, Prinal Trivedi, Jelai Wang, Stanislav O. Zakharkin

Mathematics and Statistics Faculty Research & Creative Works

Many efforts in microarray data analysis are focused on providing tools and methods for the qualitative analysis of microarray data. HDBStat! (High-Dimensional Biology-Statistics) is a software package designed for analysis of high dimensional biology data such as microarray data. It was initially developed for the analysis of microarray gene expression data, but it can also be used for some applications in proteomics and other aspects of genomics. HDBStat! provides statisticians and biologists a flexible and easy-to-use interface to analyze complex microarray data using a variety of methods for data preprocessing, quality control analysis and hypothesis testing.

Maximal Regular Boundary Value Problems In Banach-Valued Weighted Space, Ravi P. Agarwal, Veli B. Shakhmurov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to …

Second Order Dynamic Inclusions, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The theory of dynamic inclusions on a time scale is introduced, hence accommodating the special cases of differential inclusions and difference inclusions. Fixed point theory for set-valued upper semicontinuous maps, Green's functions, and upper and lower solutions are used to establish existence results for solutions of second order dynamic inclusions.

Existence And Comparison Principles For General Quasilinear Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving convex, lower semicontinuous and locally Lipschitz functionals. We provide a generalization of the fundamental notion of sub- and supersolutions on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness and extremality results.

Existence, Comparison, And Compactness Results For Quasilinear Variational-Hemivariational Inequalities, Vy Khoi Le, Dumitru Motreanu, Siegfried Carl

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of sub- and supersolutions, on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness, and extremality results.

A Quasilinearization Approach For Two Point Nonlinear Boundary Value Problems On Time Scales, Elvan Akin, Ferhan Atici. Merdivenci

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Two Simple Resistant Regression Estimators, David J. Olive

Articles and Preprints

Two simple resistant regression estimators with O_P(n^−1/2) convergence rate are presented. Ellipsoidal trimming can be used to trim the cases corresponding to predictor variables x with large Mahalanobis distances, and the forward response plot of the residuals versus the fitted values can be used to detect outliers. The first estimator uses ten forward response plots corresponding to ten different trimming proportions, and the final estimator corresponds to the “best” forward response plot. The second estimator is similar to the elemental resampling algorithm, but sets of O(n) cases are used instead of randomly …

Measuring Shared Information And Coordinated Activity In Neuronal Networks, K L. Klinkner, C R. Shalizi, Marcelo Camperi

Physics and Astronomy

Most nervous systems encode information about stimuli in the respond- ing activity of large neuronal networks. This activity often manifests itself as dynamically coordinated sequences of action potentials. Since multiple electrode recordings are now a standard tool in neuroscience research, it is important to have a measure of such network-wide behav- ioral coordination and information sharing, applicable to multiple neural spike train data. We propose a new statistic, informational coherence , which measures how much better one unit can be predicted by knowing the dynamical state of another. We argue informational coherence is a measure of association and shared information …

The Ims New Researchers' Survival Guide, Naomi Altman, David Banks, Janis Hardwick, Kathryn Roeder, Peter Craigmile, Johanna S. Hardin, Mayetri Gupta

Pomona Faculty Publications and Research

Statistics is a wonderfully diverse profession and graduate students making career choices have many options — especially in light of the dearth of students moving into the statistical sciences today. The three main career paths at the PhD level are in academics, industry/business and government. Each of these job types offers its own mix of intellectual challenges, financial reward, pressure and security. How a new researcher selects (or is selected by) a specific occupation in the statistical sciences sometimes seems more a function of luck than of conscious decision making. This consideration was one of the first concerns addressed by …

Effects Of Supplementation Of Whole Corn Germ On Reproductive Performance, Calf Performance, And Leptin Concentration In Primiparous And Mature Beef Cows, J. L. Martin, Richard J. Rasby, Dennis R. Brink, R. U. Lindquist, D. H. Keisler, Stephen D. Kachman

Department of Statistics: Faculty Publications

A 2-yr study using primiparous and multiparous, spring-calving, crossbred beef cows was conducted to evaluate the effects of supplemental whole corn germ on reproductive performance, calf performance, and serum leptin concentrations. Each year, cows were blocked by age and BCS and assigned randomly to one of three treatments: PRE (n = 115) cows received 1.14 kg/d (DM basis) of whole corn germ for approximately 45 d before calving; POST (n = 109) cows were fed 1.14 kg/d of whole corn germ for approximately 45 d after calving; and control cows (n = 118) were fed similar energy and protein from …

On The Linear Combination Of Exponential And Gamma Random Variables, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

The exact distribution of the linear combination αX + βY is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing and other areas of computer science.

Reliability For Some Bivariate Gamma Distributions, Saralees Nadarajah

Department of Statistics: Faculty Publications

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y). The algebraic form for R = Pr(X < Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when (X,Y) follows a bivariate distribution with dependence between X and Y. In particular, we derive explicit expressions for R when the joint distribution is …

On The Product And Ratio Of Laplace And Bessel Random Variables, Sarlees Nadarajah

Department of Statistics: Faculty Publications

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are Laplace and Bessel function random variables distributed independently of each other.

On The Product And Ratio Of Laplace And Bessel Random Variables, Saralees Nadarajah

Department of Statistics: Faculty Publications

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are Laplace and Bessel function random variables distributed independently of each other.

On The Product And Ratio Of Bessel Random Variables, Saralees Nadarajah, Arjun K. Gupta

Department of Statistics: Faculty Publications

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.

A Generalized Logistic Distribution, Saralees Nadarajah, Samuel Kotz

Department of Statistics: Faculty Publications

A generalized logistic distribution is proposed, based on the fact that the difference of two independent Gumbel-distributed randomvariables has the standard logistic distribution.

Session-Based Intrusion Detection System To Map Anomalous Network Traffic, Bruce Caulkins

Electronic Theses and Dissertations

Computer crime is a large problem (CSI, 2004; Kabay, 2001a; Kabay, 2001b). Security managers have a variety of tools at their disposal -- firewalls, Intrusion Detection Systems (IDSs), encryption, authentication, and other hardware and software solutions to combat computer crime. Many IDS variants exist which allow security managers and engineers to identify attack network packets primarily through the use of signature detection; i.e., the IDS recognizes attack packets due to their well-known "fingerprints" or signatures as those packets cross the network's gateway threshold. On the other hand, anomaly-based ID systems determine what is normal traffic within a network and reports …

Microarray Data From A Statistician’S Point Of View, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.