Statistics and Probability Commons^™

Jmasm27: An Algorithm For Implementing Gibbs Sampling For 2pno Irt Models (Fortran), Yanyan Sheng, Todd C. Headrick

Journal of Modern Applied Statistical Methods

A Fortran 77 subroutine is provided for implementing the Gibbs sampling procedure to a normal ogive IRT model for binary item response data with the choice of uniform and normal prior distributions for item parameters. The subroutine requires the user to have access to the IMSL library. The source code is available at http://www.siu.edu/~epse1/sheng/Fortran/, along with a stand alone executable file.

Mathmatics In Volume I Of Scripta Universitatis, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

Immanuel Velikovsky’s journal, Scripta Universitatis, edited by Albert Einstein and first published in 1923, played a significant role in the establishment of the library, and hence, Hebrew University in Jerusalem. The inaugural issue contained an article by the French mathematician Jacques Hadamard. Excerpts from Velikovsky’s diary pertaining to the rationale for the creation of the journal, and the interest in Jewish scholars such as Hadamard, are translated here.

Practical Unit-Root Analysis Using Information Criteria: Simulation Evidence, Kosei Fukuda

Journal of Modern Applied Statistical Methods

The information-criterion-based model selection method for detecting a unit root is proposed. The simulation results suggest that the performances of the proposed method are usually comparable to and sometimes better than those of the conventional unit-root tests. The advantages of the proposed method in practical applications are also discussed.

Tests For Treatment Group Equality When Data Are Nonnormal And Heteroscedastic, Robert A. Cribbie, Rand R. Wilcox, Carmen Bewell, H. J. Keselman

Journal of Modern Applied Statistical Methods

Several tests for group mean equality have been suggested for analyzing nonnormal and heteroscedastic data. A Monte Carlo study compared the Welch tests on ranked data and heterogeneous, nonparametric statistics with previously recommended procedures. Type I error rates for the Welch tests on ranks and the heterogeneous, nonparametric statistics were well controlled with a slight power advantage for the Welch tests on ranks.

A Fano-Huffman Based Statistical Coding Method, Aladdin Shamilov, Senay Asma

Journal of Modern Applied Statistical Methods

Statistical coding techniques have been used for lossless statistical data compression, applying methods such as Ordinary, Shannon, Fano, Enhanced Fano, Huffman and Shannon-Fano-Elias coding methods. A new and improved coding method is presented, the Fano-Huffman Based Statistical Coding Method. It holds the advantages of both the Fano and Huffman coding methods. It is more easily applicable than the Huffman coding methods and it is more optimal than Fano coding method. The optimality with respect to the other methods is realized on the basis of English, German, Turkish, French, Russian and Spanish.

Modeling Longitudinal Ordinal Response Variables For Educational Data, Ann A. O'Connell, Heather Levitt Doucette

Journal of Modern Applied Statistical Methods

This article presents applications for the analysis of multilevel ordinal response data through the proportional odds model. Data are drawn from the public-use Early Childhood Longitudinal Study. Results showed that gender, number of family risk characteristics, and age at kindergarten entry were associated with initial reading proficiency (0 to 5 scale). The number of family risks and age were associated with time-slopes. Three issues are highlighted: building multilevel ordinal models, interpretation of multilevel effects; and determination of predicted probabilities based on results of the multilevel proportional odds models.

Bimodality Revisited, Thomas R. Knapp

Journal of Modern Applied Statistical Methods

Degree of bimodality is an important feature of a frequency distribution, because it could suggest heterogeneity, such as polarization or two underlying distributions combined into one. The literature contains several measures of bimodality. This article attempts to summarize most of those measures, with their attendant advantages and disadvantages.

Type I Error Rates Of The Kenward-Roger Adjusted Degree Of Freedom F-Test For A Split-Plot Design With Missing Values, Miguel A. Padilla, James Algina

Journal of Modern Applied Statistical Methods

The Type I error rate of the Kenward-Roger (KR) test, implemented by PROC MIXED in SAS, was assessed through a simulation study for a one between- and one within-subjects factor split-plot design with ignorable missing values and covariance heterogeneity. The KR test controlled the Type I error well under all of the simulation factors, with all estimated Type I error rates between .040 and .075. The best control was for testing the between-subjects main effect (error rates between .041 and .057) and the worst control was for the between-by-within interaction (.040 to .075). The simulated factors had very small effects …

Comparison Of The T Vs. Wilcoxon Signed-Rank Test For Likert Scale Data And Small Samples, Gary E. Meek, Ceyhun Ozgur, Kenneth Dunning

Journal of Modern Applied Statistical Methods

The one sample t-test is compared with the Wilcoxon Signed-Rank test for identical data sets representing various Likert scales. An empirical approach is used with simulated data. Comparisons are based on observed error rates for 27,850 data sets. Recommendations are provided.

Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

The aim of this article is to obtain and compare confidence intervals for the mean of an exponential distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for parameters of exponential population are derived. Using exponential data, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with Fisher Matrix bounds method. It is shown that the proposed approximate Bayesian approach relies only on the observations. The Fisher Matrix bounds method, that uses the z-table, does not always yield the best confidence intervals, and the proposed approach often performs better.

Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade

Journal of Modern Applied Statistical Methods

Some properties of a four-parameter beta-Weibull distribution are discussed. The beta-Weibull distribution is shown to have bathtub, unimodal, increasing, and decreasing hazard functions. The distribution is applied to censored data sets on bus-motor failures and a censored data set on head-and-neck-cancer clinical trial. A simulation is conducted to compare the beta-Weibull distribution with the exponentiated Weibull distribution.

A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Oligonucleotide arrays are used in many applications. Affymetrix GeneChip arrays are widely used. Before researchers can use the information from these arrays, the raw data must be transformed and summarized into a more meaningful and usable form. One of the more popular methods for doing so is RMA (Robust Multi-array Analysis).

A problem with RMA is that the end result (estimated gene expression levels) is based on a fairly complicated process that is unusual. Specifically, there is no closed-form estimate of standard errors for the estimated gene expression levels. The current recommendation is to use a naive estimate for the …

Ets (Efficient, Transparent, And Secured) Self-Healing Service For Pervasive Computing Applications, Shameem Ahmed, Moushumi Sharmin, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

To ensure smooth functioning of numerous handheld devices anywhere anytime, the importance of self-healing mechanism cannot be overlooked. Incorporation of efficient fault detection and recovery in device itself is the quest for long but there is no existing self-healing scheme for devices running in pervasive computing environments that can be claimed as the ultimate solution. Moreover, the highest degree of transparency, security and privacy attainability should also be maintained. ETS Self-healing service, an integral part of our developing middleware named MARKS (Middleware Adaptability for Resource discovery, Knowledge usability, and Self-healing), holds promise for offering all of those functionalities.

Biomarker Evaluation Using The Controls As A Reference Population, Ying Huang, Margaret Pepe

UW Biostatistics Working Paper Series

The classification accuracy of a continuous marker is typically evaluated with the Receiver Operating Characteristic Curve. In this paper, we study an alternative conceptual framework, the "percentile value". In particular the controls only provide a reference distribution to standardize the marker. The analysis proceeds by analyzing the standardized marker only in cases. The approach is shown to be equivalent to ROC analysis. Advantages are that it provides a framework more familiar to biostatisticians and it opens up avenues for new statistical techniques in biomarker evaluation. We develop several new procedures based on this framework for comparing biomarkers and for comparing …

Potret Buram Pelayanan Kesehatan Lanjut Usia Di Indonesia, Indang Trihandini

Kesmas

Jumlah dan proporsi kelompok lanjut usia (lansia) di seluruh dunia, terus meningkat, dan cenderung menjadi masalah kesehatan dan sosial sehingga mendapat perhatian dan dukungan yang serius. Resolusi PBB no 46/ 1991, 16 Desember 1991 menghimbau agar seluruh negara di dunia memberikan hak yang layak kepada kelompok lansia. Di Indonesia, populasi lansia pada tahun 2000 (17,2 juta) meningkat 3 kali lebih besar dari pada tahun 1970 (5,3 juta). Pada tahun 2020, jumlah dan proporsi kelompok lansia di Indonesia diprediksi akan mencapai 28 juta jiwa dan 9,5%. Aspek legal telah menempatkan lansia Indonesia pada tempat yang respek dan terhormat, tetapi, kenyataan memperlihatkan …

Tantangan Pencapaian Millenium Development Goals (Mdgs) Bidang Kesehatan Di Indonesia, Budi Utomo

Kesmas

Laporan pemerintah tentang pencapaian MDGs di Indonesia sampai tahun 2002 merefleksikan komitmen dalam mensejahterakan rakyat. Kesehatan yang dijabarkan dalam berbagai indikator tujuan 4, 5, dan 6 dilaporkan membaik. Tulisan ini menelaah status pencapaian, mencari penjelasan latar belakang pencapaian, dan menilai prospek pencapaian MDGs utamanya bidang kesehatan. Hasil telaah menunjukkan sebagian besar indikator kesehatan membaik, tetapi lamban. Walau menurun, angka kematian ibu dan anak masih tinggi. Penyakit infeksi dan masalah gizi masih prevalen. Akses masyarakat terhadap pelayanan kesehatan masih rendah. Biaya masih menjadi penghambat utama pelayanan kesehatan bagi mereka yang membutuhkan. Program pemberantasan penyakit menular, termasuk HIV/AIDS, malaria, dan TB masih …

Bayesian Spatial Modeling Of Fmri Data: A Multiple-Subject Analysis, Lei Xu, Timothy Johnson, Thomas Nichols

The University of Michigan Department of Biostatistics Working Paper Series

The aim of this work is to develop a spatial model for multi-subject fMRI data. While there has been much work on univariate modeling of each voxel for single- and multi-subject data, and some work on spatial modeling for single-subject data, there has been no work on spatial models that explicitly account for intersubject variability in activation location. We use a Bayesian hierarchical spatial model to fit the data. At the first level we model "population centers" that mark the centers of regions of activation. For a given population center each subject may have zero or more associated "individual components". …

A Bayesian Hierarchical Framework For Spatial Modeling Of Fmri Data, F. Dubois Bowman, Brian S. Caffo, Susan Spear Bassett, Clinton Kilts

Johns Hopkins University, Dept. of Biostatistics Working Papers

Functional neuroimaging techniques enable investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric,neurological, and substance abuse disorders, as well as into the neural responses to their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. One may also extend voxel-level analyses by simultaneously considering the ensemble of voxels constituting an anatomically defined region of interest (ROI) or by considering means or quantiles of the ROI. In this work we present a Bayesian extension …

Covariate Adjustment In Randomized Trials With Binary Outcomes: Targeted Maximum Likelihood Estimation, Kelly L. Moore, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Covariate adjustment using linear models for continuous outcomes in randomized trials has been shown to increase efficiency and power over the unadjusted method in estimating the marginal effect of treatment. However, for binary outcomes, investigators generally rely on the unadjusted estimate as the literature indicates that covariate-adjusted estimates based on logistic regression models are less efficient. The crucial step that has been missing when adjusting for covariates is that one must integrate/average the adjusted estimate over those covariates in order to obtain the marginal effect. We apply the method of targeted maximum likelihood estimation (MLE), as presented in van der …

What Is The Best Reference Rna? And Other Questions Regarding The Design And Analysis Of Two-Color Microarray Experiments, Kathleen F. Kerr, Kyle A. Serikawa, Caimiao Wei, Mette A. Peters, Roger E. Bumgarner

UW Biostatistics Working Paper Series

The reference design is a practical and popular choice for microarray studies using two-color platforms. In the reference design, the reference RNA uses half of all array resources, leading investigators to ask: What is the best reference RNA? We propose a novel method for evaluating reference RNAs and present the results of an experiment that was specially designed to evaluate three common choices of reference RNA. We found no compelling evidence in favor of any particular reference. In particular, a commercial reference showed no advantage in our data. Our experimental design also enabled a new way to test the effectiveness …

Canonical Correlation And Correspondence Analysis Of Longitudinal Data, Jayesh Srivastava

Mathematics & Statistics Theses & Dissertations

Assessing the relationship between two sets of multivariate vectors is an important problem in statistics. Canonical correlation coefficients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. When the variables are qualitative (categorical), a technique called correspondence analysis (CA) is used. Canonical correspondence analysis (CCPA) is used to deal with the case when one set of variables is categorical and the other set is quantitative. By exploiting the interrelationships between these three techniques we first provide a theoretical basis for …

A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …

Detection And Estimation Of A Mixture In Power Law Processes For A Repairable System, Ni Wang, Paul Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

The power law process has proved to be a useful tool in characterizing the failure process of repairable systems. This paper presents a procedure for detecting and estimating a mixture of reliable and unreliable (defective) systems. The test of a mixture, based on a simple likelihood ratio, is illustrated with truncated failure data for copy machines. Bootstrap methods are used to gauge the estimation uncertainty, and optimal decisions for system replacement are determined based on the observed likelihood.

Repeatability Of Serial Carotid Intima Media Thickness Scanning On Individual Subjects, Judi Nightingale

Loma Linda University Electronic Theses, Dissertations & Projects

Background. Heart disease affects millions of Americans each year. In order to improve primary prevention, early risk identification is essential. B-mode ultrasound of the common carotid artery (CCA) intima-media thickness (IMT) assesses risk of a coronary event early in the process of plaque development. Because IMT changes are so small over time, in order to determine clinically significant versus clinically insignificant changes in IMT over a 12 month time period, a protocol is needed which can detect the least significant difference (LSD) of at least 0.030 mm.

Purpose. The purpose of this study was to develop and test a well-defined …

Uncertainty Assessment In High-Risk Environments Using Probability, Evidence Theory And Expert Judgment Elicitation, Stella Barberis Bondi

Engineering Management & Systems Engineering Theses & Dissertations

The level of uncertainty in advanced system design is assessed by comparing the results of expert judgment elicitation to probability and evidence theory. This research shows how one type of monotone measure, namely Dempster-Shafer Theory of Evidence can expand the framework of uncertainty to provide decision makers a more robust solution space. The issues imbedded in this research are focused on how the relevant predictive uncertainty produced by similar action is measured.

This methodology uses the established approach from traditional probability theory and Dempster-Shafer evidence theory to combine two classes of uncertainty, aleatory and epistemic. Probability theory provides the mathematical …

Fast Adaptive Penalized Splines, Tatyana Krivobokova, Ciprian M. Crainiceanu, Goran Kauermann

Johns Hopkins University, Dept. of Biostatistics Working Papers

This paper proposes a numerically simple routine for locally adaptive smoothing. The locally heterogeneous regression function is modelled as a penalized spline with a smoothly varying smoothing parameter modelled as another penalized spline. This is being formulated as hierarchical mixed model, with spline coe±cients following a normal distribution, which by itself has a smooth structure over the variances. The modelling exercise is in line with Baladandayuthapani, Mallick & Carroll (2005) or Crainiceanu, Ruppert & Carroll (2006). But in contrast to these papers Laplace's method is used for estimation based on the marginal likelihood. This is numerically simple and fast and …

A Flexible Semi-Parametric Approach To Estimating A Dose-Response Relationship: The Treatment Of Childhood Amblyopia. , David A. Stephens, Erica E M Moodie

COBRA Preprint Series

In a study of a dose-response relationship, flexibility in modelling is essential to capturing the treatment effect when the mean effect of other covariates is not fully understood, so that observed treatment effect is not due to the imposition of a rigid model for the relationship between response, treatment, and other variables. A semiparametric additive linear mixed (SPALM) model (Ruppert et al. 2003) provides a tractable and flexible approach to modelling the influence of potentially confounding variables. In this paper, we present pure likelihood and Bayesian versions of the SPALM model. Both methods of inference are readily implementable, but the …

A Bayesian Hierarchical Model For Spot Fluorescence In Microarrays, Federico Mattia Stefanini

COBRA Preprint Series

Microarray experiments are characterized by the presence of many sources of experimental bias and a remarkably large technical variability. The assessment of differential expression for genes transcribed into a small number of mRNA copies heavily depends on the proper quantification of background fluorescence within spot. The rough model `observed = hybridization plus background' fluorescence is at first reformulated at spot level, then it is embedded into a Bayesian hierarchical model suited for fitting control spots. The novelties of the approach include the background correction performed on the latent mean of replicated spots, and an explicit model for outlying observations at …

False Discovery Rate Analysis Of Brain Diffusion Direction Maps, Armin Schwartzman, Robert F. Dougherty, Jonathan E. Taylor

COBRA Preprint Series

Diffusion tensor imaging (DTI) is a novel modality of magnetic resonance imaging that allows non-invasive mapping of the brain’s white matter. A particular map derived from DTI measurements is a map of water principal diffusion directions, which are proxies for neural fiber directions. We consider an experiment in which diffusion direction maps were acquired for two groups of subjects. The objective of the analysis is to find regions of the brain in which the corresponding diffusion directions differ between the groups. This is attained by first computing a test statistic for the difference in direction at every brain location using …

On Comparing The Clustering Of Regression Models Method With K-Means Clustering, Li-Xuan Qin, Steven G. Self

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

Gene clustering is a common question addressed with microarray data. Previous methods, such as K-means clustering and hierarchical clustering, base gene clustering directly on the observed measurements. A new model-based clustering method, the clustering of regression models (CORM) method, bases the clustering of genes on their relationship to covariates. It explicitly models different sources of variations and bases gene clustering solely on the systematic variation. Both being partitional clustering, CORM is closely related to K-means clustering. In this paper, we discuss the relationship between the two clustering methods in terms of both model formulation and implications on other important aspects …