Statistics and Probability Commons^™

The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li

Mathematics and Statistics Faculty Publications

This work is an extensive study of the 3 different types of positive solutions of the Matukuma equation 1r2(r2ϕ′)′=−rλ−2(1+r2)λ/2ϕp,p>1,λ>0 : the E-solutions (regular at r = 0), the M-solutions (singular at r = 0) and the F-solutions (whose existence begins away from r = 0). An essential tool is a transformation of the equation into a 2-dimensional asymptotically autonomous system, whose limit sets (by a theorem of H. R. Thieme) are the limit sets of Emden–Fowler systems, and serve as a characterization of the different solutions. The emphasis lies on the study of the M …

The Not-So-Quiet Revolution: Cautionary Comments On The Rejection Of Hypothesis Testing In Favor Of A “Causal” Modeling Alternative, Daniel H. Robinson, Joel R. Levin

Journal of Modern Applied Statistical Methods

Rodgers (2010) recently applauded a revolution involving the increased use of statistical modeling techniques. It is argued that such use may have a downside, citing empirical evidence in educational psychology that modeling techniques are often applied in cross-sectional, correlational studies to produce unjustified causal conclusions and prescriptive statements.

Notes On Hypothesis Testing Under A Single-Stage Design In Phase Ii Trial, Kung-Jong Lui

Journal of Modern Applied Statistical Methods

A primary objective of a phase II trial is to determine future development is warranted for a new treatment based on whether it has sufficient activity against a specified type of tumor. Limitations exist in the commonly-used hypothesis setting and the standard test procedure for a phase II trial. This study reformats the hypothesis setting to mirror the clinical decision process in practice. Under the proposed hypothesis setting, the critical points and the minimum required sample size for a desired power of finding a superior treatment at a given α -level are presented. An example is provided to illustrate how …

Adjusted Confidence Interval For The Population Median Of The Exponential Distribution, Moustafa Omar Ahmed Abu-Shawiesh

Journal of Modern Applied Statistical Methods

The median confidence interval is useful for one parameter families, such as the exponential distribution, and it may not need to be adjusted if censored observations are present. In this article, two estimators for the median of the exponential distribution, MD, are considered and compared based on the sample median and the maximum likelihood method. The first estimator is the sample median, MD₁, and the second estimator is the maximum likelihood estimator of the median, MD_MLE. Both estimators are used to propose a modified confidence interval for the population median of the exponential distribution, MD …

A Comparison Between Unbiased Ridge And Least Squares Regression Methods Using Simulation Technique, Mowafaq M. Al-Kassab, Omar Q. Qwaider

Journal of Modern Applied Statistical Methods

The parameters of the multiple linear regression are estimated using least squares ( B̂_LS ) and unbiased ridge regression methods (B̂(KI,J)). Data was created for fourteen independent variables with four different values of correlation between these variables using Monte Carlo techniques. The above methods were compared using the mean squares error criterion. Results show that the unbiased ridge method is preferable to the least squares method.

A General Class Of Chain-Type Estimators In The Presence Of Non-Response Under Double Sampling Scheme, Sunil Kumar, Housila P. Singh, Sandeep Bhougal

Journal of Modern Applied Statistical Methods

General class chain ratio type estimators for estimating the population mean of a study variable are examined in the presence of non-response under a double sampling scheme using a factor-type estimator (FTE). Properties of the suggested estimators are studied and compared to those of existing estimators. An empirical study is carried out to demonstrate the performance of the suggested estimators; empirical results support the theoretical study.

On Scientific Research: The Role Of Statistical Modeling And Hypothesis Testing, Lisa L. Harlow

Journal of Modern Applied Statistical Methods

Comments on Rodgers (2010a, 2010b) and Robinson and Levin (2010) are presented. Rodgers (2010a) initially reported on a growing trend towards more mathematical and statistical modeling; and a move away from null hypothesis significance testing (NHST). He defended and clarified those views in his sequel. Robinson and Levin argued against the perspective espoused by Rodgers and called for more research using experimentally manipulated interventions and less emphasis on correlational research and ill-founded prescriptive statements. In this response, the goal of science and major scientific approaches are discussed as well as their strengths and shortcomings. Consideration is given to how their …

Nonlinear Trigonometric Transformation Time Series Modeling, K. A. Bashiru, O. E. Olowofeso, S. A. Owabumoye

Journal of Modern Applied Statistical Methods

The nonlinear trigonometric transformation and augmented nonlinear trigonometric transformation with a polynomial of order two was examined. The two models were tested and compared using daily mean temperatures for 6 major towns in Nigeria with different rates of missing values. The results were used to determine the consistency and efficiency of the models formulated.

Powerpack: Energy Profiling And Analysis Of High-Performance Systems And Applications, Rong Ge, Xizhou Feng, Shuaiwen Song, Hung-Ching Chang, Dong Li, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Energy efficiency is a major concern in modern high-performance computing system design. In the past few years, there has been mounting evidence that power usage limits system scale and computing density, and thus, ultimately system performance. However, despite the impact of power and energy on the computer systems community, few studies provide insight to where and how power is consumed on high-performance systems and applications. In previous work, we designed a framework called PowerPack that was the first tool to isolate the power consumption of devices including disks, memory, NICs, and processors in a high-performance cluster and correlate these measurements …

On Semigroups With Lower Semimodular Lattice Of Subsemigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The question of which semigroups have lower semimodular lattice of subsemigroups has been open since the early 1960s, when the corresponding question was answered for modularity and for upper semimodularity. We provide a characterization of such semigroups in the language of principal factors. Since it is easily seen (and has long been known) that semigroups for which Green's relation J is trivial have this property, a description in such terms is natural. In the case of periodic semigroups—a case that turns out to include all eventually regular semigroups—the characterization becomes quite explicit and yields interesting consequences. In the general case, …

Gains In Power From Structured Two-Sample Tests Of Means On Graphs, Laurent Jacob, Pierre Neuvial, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially expressed genes between two patient populations, as shifts in expression levels are expected to be coherent with the structure of graphs reflecting gene properties such as biological process, molecular function, regulation, or metabolism. For a fixed graph of interest, we demonstrate that accounting for graph structure can yield more powerful tests under the assumption of smooth distribution shift on the graph. We also investigate …

Stereotype Logit Models For High Dimensional Data, Andre Williams

Theses and Dissertations

Gene expression studies are of growing importance in the field of medicine. In fact, subtypes within the same disease have been shown to have differing gene expression profiles (Golub et al., 1999). Often, researchers are interested in differentiating a disease by a categorical classification indicative of disease progression. For example, it may be of interest to identify genes that are associated with progression and to accurately predict the state of progression using gene expression data. One challenge when modeling microarray gene expression data is that there are more genes (variables) than there are observations. In addition, the genes usually demonstrate …

Developing A Library Value Indicator For A Disciplinary Population, Jeanne M. Brown

Library Faculty Presentations

Population
- Landscape architecture studio of ten 5th year students
- Use of physical library ranges from 1- 30 times/month
- Use of virtual library ranges from 2-30x/month
- Compared to others in School of Architecture use is moderate
- They self-rate as average or above average on library skills, compared to their peers

Mengukur Kualitas Hidup Anak, Toha Muhaimin

Kesmas

Kata kualitas hidup sering dihubungkan dengan pembangunan, khususnya pembangunan manusia, yang sering dikaitkan dengan kondisi seseorang baik dalam keadaan sehat maupun sakit, untuk menunjukkan aktivitas fisik, atau kondisi seseorang dalam hidup sehari-harinya. Sebagian orang mengkaitkan istilah kualitas hidup dengan kondisi sejauh mana terpenuhinya kebutuhan dasar untuk hidup seperti sandang, pangan, papan dan pendidikan pada seseorang. Oleh karena itu, banyak penelitian mengukur kualitas hidup dengan instrumen yang berbeda-beda, termasuk mengukur kualitas hidup anak dan banyak instrumen yang telah dikembangkan. Tulisan ini mencoba membahas pengertian kualitas hidup dan cara mengukurnya, terutama pada anak. Belum ada konsensus mengukur atau menggambarkan definisi konseptual kualitas …

Assessment Of Acgh Clustering Methodologies, Serena F. Baker

Theses and Dissertations

Array comparative genomic hybridization (aCGH) is a technique for identifying duplications and deletions of DNA at specific locations across a genome. Potential objectives of aCGH analysis are the identification of (1) altered regions for a given subject, (2) altered regions across a set of individuals, and (3) clinically relevant clusters of hybridizations. aCGH analysis can be particularly useful when it identifies previously unknown clusters with clinical relevance. This project focuses on the assessment of existing aCGH clustering methodologies. Three methodologies are considered: hierarchical clustering, weighted clustering of called aCGH data, and clustering based on probabilistic recurrent regions of alteration within …

Modeling Functional Data With Spatially Heterogeneous Shape Characteristics, Ana-Maria Staicu, Ciprian M. Crainiceanu, Daniel S. Reich, David Ruppert

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set …

A Maximum Pseudo-Likelihood Approach For Estimating Species Trees Under The Coalescent Model, Liang Liu, Lili Yu, Scott V. Edwards

Biostatistics: Faculty Publications

Background

Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, …

Non-Invasive Prenatal Detection Of Trisomy 21 Using Tandem Single Nucleotide Polymorphisms, Sujana Ghanta, Michael Mitchell, Mary Ames, Mats Hidestrand, Pippa Simpson, Mary Goetsch, William Thilly, Craig Struble, Aoy Tomita-Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Screening tests for Trisomy 21 (T21), also known as Down syndrome, are routinely performed for the majority of pregnant women. However, current tests rely on either evaluating non-specific markers, which lead to false negative and false positive results, or on invasive tests, which while highly accurate, are expensive and carry a risk of fetal loss. We outline a novel, rapid, highly sensitive, and targeted approach to non-invasively detect fetal T21 using maternal plasma DNA.

Methods and Findings: Highly heterozygous tandem Single Nucleotide Polymorphism (SNP) sequences on chromosome 21 were analyzed using High-Fidelity PCR and Cycling Temperature Capillary …

Population Value Decomposition, A Framework For The Analysis Of Image Populations, Ciprian M. Crainiceanu, Brian S. Caffo, Sheng Luo, Vadim Zipunnikov

Johns Hopkins University, Dept. of Biostatistics Working Papers

Images, often stored in multidimensional arrays are fast becoming ubiquitous in medical and public health research. Analyzing populations of images is a statistical problem that raises a host of daunting challenges. The most severe challenge is that data sets incorporating images recorded for hundreds or thousands of subjects at multiple visits are massive. We introduce the population value decomposition (PVD), a general method for simultaneous dimensionality reduction of large populations of massive images. We show how PVD can seamlessly be incorporated into statistical modeling and lead to a new, transparent and fast inferential framework. Our methodology was motivated by and …

Multilevel Functional Principal Component Analysis For High-Dimensional Data, Vadim Zipunnikov, Brian Caffo, Ciprian Crainiceanu, David M. Yousem, Christos Davatzikos, Brian S. Schwartz

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose fast and scalable statistical methods for the analysis of hundreds or thousands of high dimensional vectors observed at multiple visits. The proposed inferential methods avoid the difficult task of loading the entire data set at once in the computer memory and use sequential access to data. This allows deployment of our methodology on low-resource computers where computations can be done in minutes on extremely large data sets. Our methods are motivated by and applied to a study where hundreds of subjects were scanned using Magnetic Resonance Imaging (MRI) at two visits roughly five years apart. The original data …