Multivariate Bonferroni-Type Inequalities: Theory and Applications, 1st Edition (Hardback) book cover

Multivariate Bonferroni-Type Inequalities

Theory and Applications, 1st Edition

By John Chen

Chapman and Hall/CRC

302 pages | 13 B/W Illus.

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Hardback: 9781466518438
pub: 2014-07-22
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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 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.

Table of Contents

Introduction

Multiple Extreme Values

Minimum Effective Dose

System Reliability

Education Reform and Theoretical Windows

Ruin Probability and Multiple Premiums

Martingale Inequality and Asset Portfolio

Fundamentals

Univariate Bonferroni-Type Bounds

Univariate Optimality

Multivariate Bounds

Multivariate Optimality

Multivariate Indicator Functions

Method of Indicator Functions

Moments of Bivariate Indicator Functions

Factorization of Indicator Functions

A Paradox on Factorization and Binomial

Multivariate Linear Programming Framework

Linear Programming Upper Bounds

Linear Programming Lower Bounds

Bivariate Upper Bounds

Bivariate Factorized Upper Bounds

Bivariate High-degree Upper Bounds

Bivariate Optimal Upper Bounds

Applications in Multiple Testing

Multivariate and Hybrid Upper Bounds

High-Dimension Upper Bounds

Hybrid Upper Bounds

Applications in Successive Comparisons

Bivariate Lower Bounds

Bivariate Factorized Lower Bounds

Bivariate High-degree Lower Bounds

Bivariate Optimal Factorized Bounds

Bivariate Optimal Algorithm Bounds

Applications in Seasonal Trend Analysis

Multivariate and Hybrid Lower Bounds

High-Dimension Lower Bounds

Hybrid Lower Bounds

Applications in Outlier Detection

Case Studies

Molecular Cancer Therapy

Therapeutic Window

Minimum Effective Dose with Heteroscedasticity

Simultaneous Inference with Binary Data

Post-thrombotic Syndrome and Rang Regression

Vascular Risk Assessment

Big Data Analysis

Bibliography

Index

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis