Download or read book Large scale Simultaneous Hypothesis Testing written by Bradley Efron and published by . This book was released on 2003 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Large Scale Inference written by Bradley Efron and published by Cambridge University Press. This book was released on 2012-11-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.
Download or read book Large scale Multiple Hypothesis Testing with Complex Data Structure written by Xiaoyu Dai and published by . This book was released on 2018 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, motivated by a variety of applications in medicine, bioinformatics, genomics, brain imaging, etc., a growing amount of statistical research has been devoted to large-scale multiple testing, where thousands or even greater numbers of tests are conducted simultaneously. However, due to the complexity of real data sets, the assumptions of many existing multiple testing procedures, e.g. that tests are independent and have continuous null distributions of p-values, may not hold. This poses limitations in their performances such as low detection power and inflated false discovery rate (FDR). In this dissertation, we study how to better proceed the multiple testing problems under complex data structures. In Chapter 2, we study the multiple testing with discrete test statistics. In Chapter 3, we study the discrete multiple testing with prior ordering information incorporated. In Chapter 4, we study the multiple testing under complex dependency structure. We propose novel procedures under each scenario, based on the marginal critical functions (MCFs) of randomized tests, the conditional random field (CRF) or the deep neural network (DNN). The theoretical properties of our procedures are carefully studied, and their performances are evaluated through various simulations and real applications with the analysis of genetic data from next-generation sequencing (NGS) experiments.
Download or read book Simultaneous Statistical Inference written by Thorsten Dickhaus and published by Springer Science & Business Media. This book was released on 2014-01-23 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph will provide an in-depth mathematical treatment of modern multiple test procedures controlling the false discovery rate (FDR) and related error measures, particularly addressing applications to fields such as genetics, proteomics, neuroscience and general biology. The book will also include a detailed description how to implement these methods in practice. Moreover new developments focusing on non-standard assumptions are also included, especially multiple tests for discrete data. The book primarily addresses researchers and practitioners but will also be beneficial for graduate students.
Download or read book Global Testing and Large Scale Multiple Testing for High Dimensional Covariance Structures written by Tony Cai and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Driven by a wide range of contemporary applications, statistical inference for covariance structures has been an active area of current research in high-dimensional statistics. This review provides a selective survey of some recent developments in hypothesis testing for high-dimensional covariance structures, including global testing for the overall pattern of the covariance structures and simultaneous testing of a large collection of hypotheses on the local covariance structures with false discovery proportion and false discovery rate control. Both one-sample and two-sample settings are considered. The specific testing problems discussed include global testing for the covariance, correlation, and precision matrices, and multiple testing for the correlations, Gaussian graphical models, and differential networks.
Download or read book Resampling Based Multiple Testing written by Peter H. Westfall and published by John Wiley & Sons. This book was released on 1993-01-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combines recent developments in resampling technology (including the bootstrap) with new methods for multiple testing that are easy to use, convenient to report and widely applicable. Software from SAS Institute is available to execute many of the methods and programming is straightforward for other applications. Explains how to summarize results using adjusted p-values which do not necessitate cumbersome table look-ups. Demonstrates how to incorporate logical constraints among hypotheses, further improving power.
Download or read book Multiple Testing Procedures Controlling False Discovery Rate with Applications to Genomic Data written by Iris Mirales Gauran and published by . This book was released on 2018 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent mutation studies, analyses based on protein domain positions are gaining popularity over traditional gene-centric approaches since the latter have limitations in considering the functional context that the position of the mutation provides. This presents a large-scale simultaneous inference problem, with hundreds of hypothesis tests to consider at the same time. The overarching objective of this thesis is to propose different multiple testing procedures which can address the problems posed by discrete genomic data. Specifically, we are interested in identifying significant mutation counts while controlling a given level of Type I error via False Discovery Rate (FDR) procedures. One main assumption is that the mutation counts follow a zero-inflated model in order to account for the true zeros in the count model and the excess zeros. The class of models considered is the Zero-inflated Generalized Poisson (ZIGP) distribution.
Download or read book Analysis of Error Control in Large Scale Two stage Multiple Hypothesis Testing written by Wenge Guo and published by . This book was released on 2017 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Methods for Large scale Multiple Testing Problems written by Yu Gao and published by . This book was released on 2019 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large-scale multiple testing problem simultaneously tests thousands or even millions of null hypotheses, and it is widely used in different fields, for example genetics and astronomy. An error rate serves as a measure of the performance of a testing procedure. The use of the family-wise error rate can accommodate any dependence between hypotheses, but it is often overly conservative and has limited detection power.The false discovery rate is more powerful, however not as widely used due to the requirement of independence and other reasons. In this thesis, we develop statistical methods for large-scale multiple testing problems in pharmacovigilance and genetic studies, and adopt the false discovery rate to improve the detection power by tacking mixed challenges.
Download or read book Concentration of Maxima and Fundamental Limits in High Dimensional Testing and Inference written by Zheng Gao and published by Springer Nature. This book was released on 2021-09-07 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors.
Download or read book Handbook of Multiple Comparisons written by Xinping Cui and published by CRC Press. This book was released on 2021-11-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts that include originators of some key ideas, chapters in the Handbook of Multiple Testing cover multiple comparison problems big and small, with guidance toward error rate control and insights on how principles developed earlier can be applied to current and emerging problems. Some highlights of the coverages are as follows. Error rate control is useful for controlling the incorrect decision rate. Chapter 1 introduces Tukey's original multiple comparison error rates and point to how they have been applied and adapted to modern multiple comparison problems as discussed in the later chapters. Principles endure. While the closed testing principle is more familiar, Chapter 4 shows the partitioning principle can derive confidence sets for multiple tests, which may become important as the profession goes beyond making decisions based on p-values. Multiple comparisons of treatment efficacy often involve multiple doses and endpoints. Chapter 12 on multiple endpoints explains how different choices of endpoint types lead to different multiplicity adjustment strategies, while Chapter 11 on the MCP-Mod approach is particularly useful for dose-finding. To assess efficacy in clinical trials with multiple doses and multiple endpoints, the reader can see the traditional approach in Chapter 2, the Graphical approach in Chapter 5, and the multivariate approach in Chapter 3. Personalized/precision medicine based on targeted therapies, already a reality, naturally leads to analysis of efficacy in subgroups. Chapter 13 draws attention to subtle logical issues in inferences on subgroups and their mixtures, with a principled solution that resolves these issues. This chapter has implication toward meeting the ICHE9R1 Estimands requirement. Besides the mere multiple testing methodology itself, the handbook also covers related topics like the statistical task of model selection in Chapter 7 or the estimation of the proportion of true null hypotheses (or, in other words, the signal prevalence) in Chapter 8. It also contains decision-theoretic considerations regarding the admissibility of multiple tests in Chapter 6. The issue of selected inference is addressed in Chapter 9. Comparison of responses can involve millions of voxels in medical imaging or SNPs in genome-wide association studies (GWAS). Chapter 14 and Chapter 15 provide state of the art methods for large scale simultaneous inference in these settings.
Download or read book Improved Tools for Large scale Hypothesis Testing written by Zihao Zheng and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale hypothesis testing, as one of the key statistical tools, has been widely studied and applied to high throughput bioinformatics experiments, such as high-density peptide array studies and brain image data sets. The high dimensionality and small sample size of many experiments challenge conventional statistical approaches, including those aiming to control the false discovery rate (FDR). Motivated by this, in this dissertation, I develop several improved statistical and computational tools for large-scale hypothesis testing. The first method, MixTwice, advances an empirical-Bayesian tool that computes local false discovery rate statistics when provided with data on estimated effects and estimated standard errors. I also extend this method from two group comparison problems to multiple group comparison settings and develop a generalized method called MixTwice-ANOVA. The second method GraphicalT calculates local FDRs semiparametrically using available graph-associated information. The first method, MixTwice, introduces an empirical-Bayes approach that involves the estimation of two mixing distributions, one on underlying effects and one on underlying variance parameters. Provided with the estimated effect sizes and estimated errors, MixTwice estimates the mixing distribution and calculates the local false discovery rates via nonparametric MLE and constrained optimization with unimodal shape constraint of the effect distribution. Numerical experiments show that MixTwice can accurately estimate generative parameters and have good testing operating characteristics. Applied to a high-density peptide array, it powerfully identifies non-null peptides to recover meaningful peptide markers when the underlying signal is weak, and has strong reproducibility properties when the underlying signal is strong. The second contribution of this dissertation generalizes MixTwice from scenarios comparing two conditions to scenarios comparing multiple groups. Similar to MixTwice, MixTwice-ANOVA takes numerator and denominator statistics of F test to estimate two underlying mixing distributions. Compared with other large-scale testing tools for one-way ANOVA settings, MixTwice-ANOVA has better power properties and FDR control through numerical experiments. Applied to the peptide array study comparing multiple Sjogren-disease (SjD) populations, the proposed approach discovers meaningful epitope structure and novel scientific findings on Sjogren disease. Numerical experiments support evaluation among testing tools. Besides the methodology contribution of MixTwice in large-scale testing, I also discuss generalized evaluation and computational aspects. For the former part, I propose an evaluation metric, in additional to FDR control, power, etc., called reproducibility, to provide a practical guide for different testing tools. For the latter part, I borrow the idea from pool adjacent violator algorithm (PAVA) and advance a computational algorithm called EM-PAVA to solve nonparametric MLE with isotonic partial order constraint. This algorithm is discussed through theoretical guarantees and computational performances. The last contribution of this dissertation deals with large-scale testing problems with graph-associated data. Different from many studies that incorporate the graph-associated information through detailed modeling specifications, GraphicalT provides a semiparametric way to calculate the local false discovery rates using available auxiliary data graph. The method shows good performance in synthetic examples and in a brain-imaging problem from the study of Alzheimer's disease.
Download or read book Using the False Discovery Rate Criterion for Simultaneous Hypothesis Testing in Epidemiological Research written by Anat Reiner and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Inference for Gene Expression and Proteomics written by Kim-Anh Do and published by Cambridge University Press. This book was released on 2006-07-24 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expert overviews of Bayesian methodology, tools and software for multi-platform high-throughput experimentation.
Download or read book A New Approach for Large Scale Multiple Testing with Application to FDR Control for Graphically Structured Hypotheses written by Wenge Guo and published by . This book was released on 2018 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Testing Statistical Hypotheses with Given Reliability written by Kartlos Joseph Kachiashvili and published by Cambridge Scholars Publishing. This book was released on 2023-06-02 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the branch of statistical science which pertains to the theory of hypothesis testing. This involves deciding on the plausibility of two or more hypothetical models based on some data. This work will be both interesting and useful for professional and beginner researchers and practitioners of many fields, who are interested in the theoretical and practical issues of the direction of mathematical statistics, namely, in statistical hypothesis testing. It will also be very useful for specialists of different fields for solving suitable problems at the appropriate level, as the book discusses in detail many important practical problems and provides detailed algorithms for their solutions.
Download or read book A Mixture Model Approach to Empirical Bayes Testing and Estimation written by Omkar Muralidharan and published by Stanford University. This book was released on 2011 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.
