Physical Sciences and Mathematics Commons^™

Nonparametric Bayesian Multiple Comparisons For Dependence Parameter In Bivariate Exponential Populations, M. Masoom Ali, J. S. Cho, Munni Begum

Journal of Modern Applied Statistical Methods

A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied. A simple method for pairwise comparisons of these parameters is also suggested. The methodology by Gopalan and Berry (1998) is extended using Dirichlet process priors, applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through a Markov Chain Monte Carlo, Gibbs sampling, due to the intractability of analytic evaluation. The process of MCP for the dependent parameters of bivariate exponential populations is illustrated with a numerical …

Entropy Criterion In Logistic Regression And Shapley Value Of Predictors, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Entropy criterion is used for constructing a binary response regression model with a logistic link. This approach yields a logistic model with coefficients proportional to the coefficients of linear regression. Based on this property, the Shapley value estimation of predictors’ contribution is applied for obtaining robust coefficients of the linear aggregate adjusted to the logistic model. This procedure produces a logistic regression with interpretable coefficients robust to multicollinearity. Numerical results demonstrate theoretical and practical advantages of the entropy-logistic regression.

Comparison Of Some Simple Estimators Of The Lognormal Parameters Based On Censored Samples, Baklizi Ayman, Mohammed Al-Haj Ebrahem

Journal of Modern Applied Statistical Methods

Point estimation of the parameters of the lognormal distribution with censored data is considered. The often employed maximum likelihood estimator does not exist in closed form and iterative methods that require very good starting points are needed. In this article, some techniques of finding closed form estimators to this situation are presented and extended. An extensive simulation study is carried out to investigate and compare the performance of these techniques. The results show that some of them are highly efficient as compared with the maximum likelihood estimator.

Statistical Pronouncements V, Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

Properties Of The Gar(1) Model For Time Series Of Counts, Vasiliki Karioti, Chrys Caroni

Journal of Modern Applied Statistical Methods

Models for time series count data include several proposed by Zeger and Qaqish (1988), subsequently generalized into the GARMA family. The GAR(1) model is examined in detail. The maximum likelihood estimation of the parameters will be discussed and the properties of Pearson and randomized residuals will be examined.

Variance Estimation And Construction Of Confidence Intervals For Gee Estimator, Shenghai Zhang, Mary E. Thompson

Journal of Modern Applied Statistical Methods

The sandwich estimator, also known as the robust covariance matrix estimator, has achieved increasing use in the statistical literature as well as with the growing popularity of generalized estimating equations (GEE). A modified sandwich variance estimator is proposed, and its consistency and efficiency are studied. It is compared with other variance estimators, such as a model based estimator, the sandwich estimator and a corrected sandwich estimator. Confidence intervals for regression parameters based on these estimators are discussed. Simulation studies using clustered data to compare the performance of variance estimators are reported.

Jmasm22: A Convenient Way Of Generating Normal Random Variables Using Generalized Exponential Distribution, Debasis Kundu, Anubhav Manglick

Journal of Modern Applied Statistical Methods

A convenient method to generate normal random variable using a generalized exponential distribution is proposed. The new method is compared with the other existing methods and it is observed that the proposed method is quite competitive with most of the existing methods in terms of the K − S distances and the corresponding p-values.

A Combined Individuals And Moving Range Control Chart, Michael B. C. Khoo, S. H. Quah, C. K. Ch'ng

Journal of Modern Applied Statistical Methods

An individuals control chart is usually used to monitor shifts in the process mean when it is not possible to form subgroups. The moving range of two successive process measures is used as the basis for estimating the process variability. Similar to the case of the X − R and X − S charts, the individualsmoving range (I-MR) charts are used simultaneously in the monitoring of the process mean and variance respectively for individual observations, requiring maintaining two different charts. In this article, a new approach is suggested where the measurements of both the process mean and variance are plotted …

A Combined Standard Deviation Based Data Clustering Algorithm, Kuttiannan Thangavel, Durairaj Ashok Kumar

Journal of Modern Applied Statistical Methods

The clustering problem has been widely studied because it arises in many knowledge management oriented applications. It aims at identifying the distribution of patterns and intrinsic correlations in data sets by partitioning the data points into similarity clusters. Traditional clustering algorithms use distance functions to measure similarity centroid, which subside the influences of data points. Hence, in this article a novel non-distance based clustering algorithm is proposed which uses Combined Standard Deviation (CSD) as measure of similarity. The performance of CSD based K-means approach, called K-CSD clustering algorithm, is tested on synthetic data sets. It compared favorably to widely used …

The Use Of Hierarchical Ancova In Curriculum Studies, Show-Mann Liou, Chao-Ying Joanne Peng

Journal of Modern Applied Statistical Methods

Many educational studies are carried out in intact settings, such as classrooms or groups in which individual data were collected before and after a treatment. Researchers advocate either the use of individual scores as the unit of analysis or class means. Both approaches suffer from conceptual and methodological limitations. In this article, the use of hierarchical ANCOVA for analyzing quasiexperimental data including baseline measures is designed and promoted. It is illustrated with a realworld data set collected from a curriculum study. Results showed that the hierarchical ANCOVA is a conceptually and methodologically sound approach, and is better than ANCOVA based …

Variational Analysis Of Evolution Inclusions, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to optimization problems of the Bolza and Mayer types for evolution systems governed by nonconvex Lipschitzian differential inclusions in Banach spaces under endpoint constraints described by finitely many equalities and inequalities. with generally nonsmooth functions. We develop a variational analysis of such roblems mainly based on their discrete approximations and the usage of advanced tools of generalized differentiation satisfying comprehensive calculus rules in the framework of Asplund (and hence any reflexive Banach) spaces. In this way we establish extended results on stability of discrete approximations (with the strong W^1,2-convergence of optimal solutions under consistent perturbations of …

Optimization And Equilibrium Problems With Equilibrium Constraints In Infinite-Dimensional Spaces, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern variational f).nalysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as MPECs (mathematical programs with equilibrium constraints) and EPECs (equilibrium problems with equilibrium constraints) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The …

Photoionized HΒ Emission In Ngc 5548: It Breathes!, Edward M. Cackett, Keith Horne

Physics and Astronomy Faculty Research Publications

Emission-line regions in active galactic nuclei (AGNs) and other photoionized nebulae should become larger in size when the ionizing luminosity increases. This `breathing' effect is observed for the Hβ emission in NGC 5548 by using Hβ and optical continuum light curves from the 13-yr (1989-2001) AGN Watch monitoring campaign. To model the breathing, we use two methods to fit the observed light curves in detail: (i) parametrized models and, (ii) the MEMECHO reverberation-mapping code. Our models assume that optical continuum variations track the ionizing radiation, and that the Hβ variations respond with time-delays τ due to light travel-time. By fitting …

A Database And Tool, Im Browser, For Exploring And Integrating Emerging Gene And Protein Interaction Data For Drosophila, Svetlana Pacifico, Guozhen Liu, Stephen Guest, Jodi R. Parrish, Farshad Fotouhi, Russell L. Finley Jr

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Biological processes are mediated by networks of interacting genes and proteins. Efforts to map and understand these networks are resulting in the proliferation of interaction data derived from both experimental and computational techniques for a number of organisms. The volume of this data combined with the variety of specific forms it can take has created a need for comprehensive databases that include all of the available data sets, and for exploration tools to facilitate data integration and analysis. One powerful paradigm for the navigation and analysis of interaction data is an interaction graph or map that represents proteins …

Notes For Mat 7500 – Winter '93, Revised Winter '06, David Handel

Mathematics Faculty Research Publications

These notes developed from a one semester course at Wayne State University, taught several times in the last three decades of the 1900s. The subject matter is analysis on manifolds, consisting of the theory of smooth manifolds, differential forms, integration of forms, the generalized Stokes' Theorem, de Rham cohomology, and some related topics. The course is intended for first or second year graduate students in Mathematics with a background in Advanced Calculus, General Topology, linear algebra (including quotient spaces), and a little elementary group theory (including some familiarity with the symmetric groups). Given the above background, the notes are self-contained. …

Decentralized Convex-Type Equilibrium In Nonconvex Models Of Welfare Economics Via Nonlinear Prices, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern tools of variational analysis to equilibrium models of welfare economics involving nonconvex economies with infinite-dimensional commodity spaces. The main results relate to generalized/ extended second welfare theorems ensuring an equilibrium price support at Pareto optimal allocations. Based on advanced tools of generalized differentiation, we establish refined results of this type with the novel usage of nonlinear prices at the three types to optimal allocations: weak Pareto, Pareto, and strong Pareto. The usage of nonlinear (vs. standard linear) prices allow us to decentralized price equilibria in fully nonconvex models similarly to linear prices …

Limited Proteolysis Of Human Histone Deacetylase 1, Nayana Kamath, Paulina Karwowska-Desaulniers, Mary Kay H. Pflum

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Histone deacetylase (HDAC) proteins are associated with cell proliferation, differentiation, apoptosis, and cancer. Specifically, HDAC1 is linked with cell growth, a hallmark of cancer formation. HDAC1 is a phosphoprotein and phosphorylation at S421 and S423 promotes HDAC1 enzymatic activity and protein association. While single and double point mutants of HDAC1 at S421 and S423 appear functionally similar, the evidence suggests that HDAC1 is phosphorylated simultaneously at both S421 and S423 in vivo. Additional experiments are necessary to probe the role of double phosphorylation of HDAC1 at S421 and S423.

Results

To characterize HDAC1 phosphorylation at S421 and S423, …

K-Spmm: A Database Of Murine Spermatogenic Promoters Modules & Motifs, Yi Lu, Adrian E. Platts, G Charles Ostermeier, Stephen A. Krawetz

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Understanding the regulatory processes that coordinate the cascade of gene expression leading to male gamete development has proven challenging. Research has been hindered in part by an incomplete picture of the regulatory elements that are both characteristic of and distinctive to the broad population of spermatogenically expressed genes.

Description

K-SPMM, a database of murine Spermatogenic Promoters Modules and Motifs, has been developed as a web-based resource for the comparative analysis of promoter regions and their constituent elements in developing male germ cells. The system contains data on 7,551 genes and 11,715 putative promoter regions …

Fm-Test: A Fuzzy-Set-Theory-Based Approach To Differential Gene Expression Data Analysis, Lily R. Liang, Shiyong Lu, Xuena Wang, Yi Lu, Vinay Mandal, Dorrelyn Patacsil, Deepak Kumar

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Microarray techniques have revolutionized genomic research by making it possible to monitor the expression of thousands of genes in parallel. As the amount of microarray data being produced is increasing at an exponential rate, there is a great demand for efficient and effective expression data analysis tools. Comparison of gene expression profiles of patients against those of normal counterpart people will enhance our understanding of a disease and identify leads for therapeutic intervention.

Results

In this paper, we propose an innovative approach, fuzzy membership test (FM-test), based on fuzzy set theory to identify disease associated genes from microarray …

Statistical Pronouncements Iv, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

The Quartzite Problem Revisited, Jeffrey L. Howard

Environmental Science and Geology Faculty Research Publications

A review of past terminology and previous petrological studies suggests that quartzite should be classified descriptively as both a sedimentary and a metamorphic rock. Quartzite is identified in the field as a quartz‐rich rock (exclusive of chert and vein quartz) that is exceptionally hard and, when broken by a rock hammer, fractures irregularly through both grains and cement (where present) to form an irregular or conchoidal fracture surface. Quartzite is differentiated from quartzose sandstone (arenite), which is softer and fractures around individual grains, and from chert and vein quartz by a bright vitreous luster. Quartzite is classified further on the …

Comparison Of Statistical Tests In Logistic Regression: The Case Of Hypernatreamia, Stylianos Katsaragakis, Christos Koukouvinos, Stella Stylianou, Eleni-Maria Theodoraki, Eleni-Maria Theodoraki

Journal of Modern Applied Statistical Methods

The logistic regression has become an integral component of any medical data analysis concerning binary responses. The main issue rising after the adaptation of the final model is its goodness-of-fit. The fit of the model is assessed via the overall measures and summary statistics and comparing them in the case of hypernateamia.

An Estimator Of Intervention Effect On Disease Severity, David Siev

Journal of Modern Applied Statistical Methods

When a medical intervention prevents a dichotomous outcome, the size of its effect is often estimated with the prevented fraction. Some interventions may reduce the severity of an outcome without entirely preventing it. To quantify the effect of a severity-moderating intervention, a measure termed the mitigated fraction (MF) is proposed. MF has broad applicability, because it measures the overlap of two empirical distributions based on their stochastic ordering. It is also useful in the specific context of medical interventions, because it shares certain structural and functional features with the prevented fraction. The two measures may be applied together …

Bootstrap Intervals Of The Parameters Of Lognormal Distribution Using Power Rule Model And Accelerated Life Tests, Mohammed Al-Haj Ebrahem

Journal of Modern Applied Statistical Methods

Assumed that the distribution of the lifetime of any unit follows a lognormal distribution with parameters μ and σ . Also, assume that the relationship between μ and the stress level V is given by the power rule model. Several types of bootstrap intervals of the parameters were studied and their performance was studied using simulations and compared in term of attainment of the nominal confidence level, symmetry of lower and upper error rates and the expected width. Conclusions and recommendations are given.

Large Sample And Bootstrap Intervals For The Gamma Scale Parameter Based On Grouped Data, Ayman Baklizi, Amjad Al-Nasser

Journal of Modern Applied Statistical Methods

Interval estimation of the scale parameter of the gamma distribution using grouped data is considered in this article. Exact intervals do not exist and approximate intervals are needed Recently, Chen and Mi (2001) proposed alternative approximate intervals. In this article, some bootstrap and jackknife type intervals are proposed. The performance of these intervals is investigated and compared. The results show that some of the suggested intervals have a satisfactory statistical performance in situations where the sample size is small with heavy proportion of censoring.

A Comparison Of The Spearman-Brown And Flanagan-Rulon Formulas For Split Half Reliability Under Various Variance Parameter Conditions, David A. Walker

Journal of Modern Applied Statistical Methods

Differences between the Spearman-Brown and Flanagan-Rulon formulas are examined when the variance parameters for two halves of a test had the following ratios: 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0 and also had a correlation between the two halves of a test at 1.00, .95, .90, .80, .70, .60, .50, .40, .30, .20, .10, .05. It was found that use of the Spearman-Brown formula to estimate the population ρ when the ratio between the standard deviations on two halves of a test is disparate, or beyond .9 to 1.1, was not warranted. Applied and theoretical examples …

Restricted Quasi-Independent Model Resolves Paradoxical Behaviors Of Cohen’S Kappa, Vicki Stover Hertzberg, Frank Xu, Michael Haber

Journal of Modern Applied Statistical Methods

Cohen’s kappa, an index of inter-rater agreement, behaves paradoxically in 2×2 tables. λ_A is derived, an index from the restricted quasi-independent model for 2×2 tables. Simulation studies are used to demonstrate λ_A has superior performance compared to Scott’s pi. Moreover, λ_A does not show paradoxical behavior for 2×2 tables.

Maximum Tests Are Adaptive Permutation Tests, Markus Neuhäeuser, Ludwig A. Hothorn

Journal of Modern Applied Statistical Methods

In some areas, e.g., statistical genetics, it is common to apply a maximum test, where the maximum of several competing test statistics is used as a new statistic, and the permutation distribution of the maximum is used for inference. Here, it is shown that maximum tests are special cases of adaptive permutation tests. The 30-year old idea of adaptive statistical tests is more flexible than previously thought when permutation tests are used, and the selector statistic is calculated for every permutation. Because the independence between the selector and the test statistics is no longer needed, the test statistics themselves can …

Inferences About The Components Of A Generalized Additive Model, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

A method for making inferences about the components of a generalized additive model is described. It is found that a variation of the method, based on means, performs well in simulations. Unlike many other inferential methods, switching from a mean to a 20% trimmed mean was found to offer little or no advantage in terms of both power and controlling the probability of a Type I error.

The Individuals Control Chart In Case Of Non-Normality, BetüL Kan, Berna Yazici

Journal of Modern Applied Statistical Methods

This article examines the effects of non-normality as measured by skewness and provides an alternative method of designing individuals control chart with non-normal distributions. A skewness correction method for constructing the individuals control chart is provided. An example of thickness of biscuit process is presented to illustrate the individuals control chart limits.