Multivariate Bonferroni-Type Inequalities: Theory and Applications

Author:   John Chen
Publisher:   Taylor & Francis Ltd
ISBN:  

9780367378523


Pages:   302
Publication Date:   05 September 2019
Format:   Paperback
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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Multivariate Bonferroni-Type Inequalities: Theory and Applications


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Overview

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.

Full Product Details

Author:   John Chen
Publisher:   Taylor & Francis Ltd
Imprint:   CRC Press
Weight:   0.562kg
ISBN:  

9780367378523


ISBN 10:   0367378523
Pages:   302
Publication Date:   05 September 2019
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Introduction. Fundamentals. Multivariate Indicator Functions. Multivariate Linear Programming Framework. Bivariate Upper Bounds. Multivariate and Hybrid Upper Bounds. Bivariate Lower Bounds. Multivariate and Hybrid Lower Bounds. Case Studies. Bibliography. Index.

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Chen, John

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