
Multivariate Bonferroni-Type Inequalities
Theory and Applications
John Chen(Author)
CRC Press
1st Edition
Published on 22. July 2014
Book
Hardback
302 pages
978-1-4665-1843-8 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
Bosa Roca
United States
Publishing group
Taylor & Francis Inc
Target group
Professional and scholarly
Professional Practice & Development
Illustrations
20 b/w images
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 21 mm
Weight
622 gr
ISBN-13
978-1-4665-1843-8 (9781466518438)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Book
09/2019
1st Edition
Chapman & Hall/CRC
€96.10
Shipment within 15-20 days

E-Book
04/2016
1st Edition
Chapman & Hall/CRC
€89.99
Available for download

E-Book
04/2016
1st Edition
Chapman and Hall
€89.99
Available for download
Person
Chen, John
Content
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.