Multivariate Bonferroni Type Inequalities

Author : John Chen
Publisher : CRC Press
Page : 302 pages
File Size : 42,8 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466518452

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Multivariate Bonferroni-Type Inequalities by John Chen Pdf

Multivariate Bonferroni-Type Inequalities: Theory and Applications presents a systematic account of research discoveries on multivariate Bonferroni-type inequalities published in the past decade. The emergence of new bounding approaches pushes the conventional definitions of optimal inequalities and demands new insights into linear and Frechet optimality. The book explores these advances in bounding techniques with corresponding innovative applications. It presents the method of linear programming for multivariate bounds, multivariate hybrid bounds, sub-Markovian bounds, and bounds using Hamilton circuits. The first half of the book describes basic concepts and methods in probability inequalities. The author introduces the classification of univariate and multivariate bounds with optimality, discusses multivariate bounds using indicator functions, and explores linear programming for bivariate upper and lower bounds. The second half addresses bounding results and applications of multivariate Bonferroni-type inequalities. The book shows how to construct new multiple testing procedures with probability upper bounds and goes beyond bivariate upper bounds by considering vectorized upper and hybrid bounds. It presents an optimization algorithm for bivariate and multivariate lower bounds and covers vectorized high-dimensional lower bounds with refinements, such as Hamilton-type circuits and sub-Markovian events. The book concludes with applications of probability inequalities in molecular cancer therapy, big data analysis, and more.

Author : John Chen
Publisher : CRC Press
Page : 304 pages
File Size : 43,5 Mb
Release : 2014-07-22
Category : Mathematics
ISBN : 9781466518438

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Multivariate Bonferroni-Type Inequalities by John Chen Pdf

Multivariate Bonferroni-Type Inequalities: Theory and Applications presents a systematic account of research discoveries on multivariate Bonferroni-type inequalities published in the past decade. The emergence of new bounding approaches pushes the conventional definitions of optimal inequalities and demands new insights into linear and Fréchet optimality. The book explores these advances in bounding techniques with corresponding innovative applications. It presents the method of linear programming for multivariate bounds, multivariate hybrid bounds, sub-Markovian bounds, and bounds using Hamilton circuits. The first half of the book describes basic concepts and methods in probability inequalities. The author introduces the classification of univariate and multivariate bounds with optimality, discusses multivariate bounds using indicator functions, and explores linear programming for bivariate upper and lower bounds. The second half addresses bounding results and applications of multivariate Bonferroni-type inequalities. The book shows how to construct new multiple testing procedures with probability upper bounds and goes beyond bivariate upper bounds by considering vectorized upper and hybrid bounds. It presents an optimization algorithm for bivariate and multivariate lower bounds and covers vectorized high-dimensional lower bounds with refinements, such as Hamilton-type circuits and sub-Markovian events. The book concludes with applications of probability inequalities in molecular cancer therapy, big data analysis, and more.

Author : John Chen
Publisher : Unknown
Page : 0 pages
File Size : 40,7 Mb
Release : 2016
Category : Distribution (Probability theory)
ISBN : OCLC:1156475992

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Multivariate Bonferroni-Type Inequalities by John Chen Pdf

Multivariate Bonferroni-Type Inequalities: Theory and Applications presents a systematic account of research discoveries on multivariate Bonferroni-type inequalities published in the past decade. The emergence of new bounding approaches pushes the conventional definitions of optimal inequalities and demands new insights into linear and Frechet optimality. The book explores these advances in bounding techniques with corresponding innovative applications. It presents the method of linear programming for multivariate bounds, multivariate hybrid bounds, sub-Markovian bounds, and bounds using Hamilton circuits. The first half of the book describes basic concepts and methods in probability inequalities. The author introduces the classification of univariate and multivariate bounds with optimality, discusses multivariate bounds using indicator functions, and explores linear programming for bivariate upper and lower bounds. The second half addresses bounding results and applications of multivariate Bonferroni-type inequalities. The book shows how to construct new multiple testing procedures with probability upper bounds and goes beyond bivariate upper bounds by considering vectorized upper and hybrid bounds. It presents an optimization algorithm for bivariate and multivariate lower bounds and covers vectorized high-dimensional lower bounds with refinements, such as Hamilton-type circuits and sub-Markovian events. The book concludes with applications of probability inequalities in molecular cancer therapy, big data analysis, and more.

Author : Janos Galambos,Italo Simonelli
Publisher : Probability and Its Applications
Page : 288 pages
File Size : 40,5 Mb
Release : 1996-08-09
Category : Mathematics
ISBN : UOM:39015038528868

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Bonferroni-type Inequalities with Applications by Janos Galambos,Italo Simonelli Pdf

Bonferroni-Type Inequalities with Applications presents a large variety of extensions of the methods of inclusion and exclusion. Both methods for generating and methods for proof of such inequalities are discussed. The inequalities are utilized for finding classical probability estimates to modern extreme value theory and combinatorial counting to random subset selection. Applications are given in prime number theory, growth of digits in different algorithms, and in statistics such as estimates of confidence levels of simultaneous interval estimation. The prerequisites include the basic concepts of probability theory and familiarity with combinatorial arguments.

Author : Y. L. Tong
Publisher : Academic Press
Page : 256 pages
File Size : 54,9 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483269214

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Probability Inequalities in Multivariate Distributions by Y. L. Tong Pdf

Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.

Author : Samuel Kotz,N. Balakrishnan,Norman L. Johnson
Publisher : John Wiley & Sons
Page : 752 pages
File Size : 41,9 Mb
Release : 2004-04-05
Category : Mathematics
ISBN : 9780471654032

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Continuous Multivariate Distributions, Volume 1 by Samuel Kotz,N. Balakrishnan,Norman L. Johnson Pdf

Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.

Author : J. Galambos,Imre Kátai
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401128179

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Probability Theory and Applications by J. Galambos,Imre Kátai Pdf

This volume contains twenty-two original contributions by leading scientists in many important areas of probability theory and its applications. The material also includes significant new results. Together this collection of papers provides a good state-of-the-art survey of current research in the following areas: inequalities; limit theorems; renewal theory and reliability theory; characterizations of distributions; infinite divisibility of polynomials of normal variables; limiting distributions for order statistics; stochastic processes; functional equations in engineering model building; and probabilistic number theory.

Author : H.N. Nagaraja,Pranab K. Sen,Donald F. Morrison
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239901

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Statistical Theory and Applications by H.N. Nagaraja,Pranab K. Sen,Donald F. Morrison Pdf

Professor Herbert A. David of Iowa State University will be turning 70 on December 19, 1995. He is reaching this milestone in life with a very distinguished career as a statistician, educator and administrator. We are bringing out this volume in his honor to celebrate this occasion and to recognize his contributions to order statistics, biostatistics and design of experiments, among others; and to the statistical profession in general. With great admiration, respect and pleasure we dedicate this festschrift to Professor Herbert A. David, also known as Herb and H.A. among his friends, colleagues and students. When we began this project in Autumn 1993 and contacted potential contributors from the above group, the enthu siasm was phenomenal. The culmination of this collective endeavor is this volume that is being dedicated to him to celebrate his upcoming birthday. Several individuals have contributed in various capacities to the success ful completion of this project. We sincerely thank the authors of the papers appearing here. Without their dedicated work, we would just have this pref ace! Many of them have served as (anonymous) referees as well. In addition, we are thankful to the following colleagues for their time and advice: John Bunge (Cornell), Z. Govindarajulu (Kentucky), John Klein (Medical U.

Author : CH. A. Charalambides,M.V. Koutras,N. Balakrishnan
Publisher : CRC Press
Page : 665 pages
File Size : 55,7 Mb
Release : 2000-09-21
Category : Mathematics
ISBN : 9781420036084

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Probability and Statistical Models with Applications by CH. A. Charalambides,M.V. Koutras,N. Balakrishnan Pdf

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili

Author : Anonim
Publisher : Unknown
Page : 512 pages
File Size : 40,7 Mb
Release : 1998
Category : Mathematics
ISBN : UOM:39015056608626

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Studia Scientiarum Mathematicarum Hungarica by Anonim Pdf

Author : John Tuhao Chen,Clement Lee,Lincy Y. Chen
Publisher : CRC Press
Page : 315 pages
File Size : 40,9 Mb
Release : 2024-08-06
Category : Business & Economics
ISBN : 9781040096307

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Statistical Prediction and Machine Learning by John Tuhao Chen,Clement Lee,Lincy Y. Chen Pdf

Written by an experienced statistics educator and two data scientists, this book unifies conventional statistical thinking and contemporary machine learning framework into a single overarching umbrella over data science. The book is designed to bridge the knowledge gap between conventional statistics and machine learning. It provides an accessible approach for readers with a basic statistics background to develop a mastery of machine learning. The book starts with elucidating examples in Chapter 1 and fundamentals on refined optimization in Chapter 2, which are followed by common supervised learning methods such as regressions, classification, support vector machines, tree algorithms, and range regressions. After a discussion on unsupervised learning methods, it includes a chapter on unsupervised learning and a chapter on statistical learning with data sequentially or simultaneously from multiple resources. One of the distinct features of this book is the comprehensive coverage of the topics in statistical learning and medical applications. It summarizes the authors’ teaching, research, and consulting experience in which they use data analytics. The illustrating examples and accompanying materials heavily emphasize understanding on data analysis, producing accurate interpretations, and discovering hidden assumptions associated with various methods. Key Features: Unifies conventional model-based framework and contemporary data-driven methods into a single overarching umbrella over data science. Includes real-life medical applications in hypertension, stroke, diabetes, thrombolysis, aspirin efficacy. Integrates statistical theory with machine learning algorithms. Includes potential methodological developments in data science.

Author : Fred. M. Hoppe
Publisher : CRC Press
Page : 576 pages
File Size : 44,5 Mb
Release : 2021-10-01
Category : Mathematics
ISBN : 9781000104929

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Multiple Comparisons, Selection and Applications in Biometry by Fred. M. Hoppe Pdf

Aims to provide in-depth descriptions of the latest developments in multiple comparison methods and selection procedures, while emphasizing biometry. This text is published in honour of the 70th birthday of Charles W. Dunnett - a pioneer in statistical methodology.

Author : Karl C. Mosler
Publisher : IMS
Page : 414 pages
File Size : 54,8 Mb
Release : 1991
Category : Education
ISBN : 0940600269

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Stochastic Orders and Decision Under Risk by Karl C. Mosler Pdf

Author : Anonim
Publisher : Unknown
Page : 634 pages
File Size : 45,8 Mb
Release : 2001
Category : Mathematical models
ISBN : UOM:39015048294550

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Journal of Applied Probability by Anonim Pdf

Author : Eyüp Çetin,Hilal Özen
Publisher : Springer Nature
Page : 286 pages
File Size : 46,7 Mb
Release : 2023-12-29
Category : Business & Economics
ISBN : 9789819959648

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Healthcare Policy, Innovation and Digitalization by Eyüp Çetin,Hilal Özen Pdf

This book takes a deep look at healthcare in today’s post-pandemic world. It combines both theory and application to reflect a new era for healthcare. The need for innovation, digitalization, and enhanced policies in healthcare has never been greater than it is today. Taking this need into consideration, this book offers a multidisciplinary approach to healthcare, in both managerial and clinical views. Since the book combines both qualitative and quantitative studies about healthcare, readers will receive a broad view of healthcare issues and policies in today’s world.