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An Introduction to Random Sets

An Introduction to Random Sets by Hung T. Nguyen
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GENERALITIES ON PROBABILITY
Survey Sampling Revisited
Mathematical Models for Random Phenomena
Random Elements
Distribution Functions of Random Variables
Distribution Functions of Random Vectors
Exercises

SOME RANDOM SETS IN STATISTICS
Probability Sampling Designs
Confidence Regions
Robust Bayesian Statistics
Probability Density Estimation
Coarse Data Analysis
Perception-Based Information
Stochastic Point Processes
Exercises

FINITE RANDOM SETS
Random Sets and Their Distributions
Set-Valued Observations
Imprecise Probabilities
Decision Making with Random Sets
Exercises

RANDOM SETS AND RELATED UNCERTAINTY MEASURES
Some Set Functions
Incidence Algebras
Cores of Capacity Functionals
Exercises

RANDOM CLOSED SETS
Introduction
The Hit-or-Miss Topology
Capacity Functionals
Notes on the Choquet Theorem on Polish Spaces
Exercises

THE CHOQUET INTEGRAL
Some Motivations
The Choquet Integral
Radon-Nikodym Derivatives
Exercises

CHOQUET WEAK CONVERGENCE
Stochastic Convergence of Random Sets
Convergence in Distribution
Weak Convergence of Capacity Functionals
Exercises

SOME ASPECTS OF STATISTICAL INFERENCE WITH COARSE DATA
Expectations and Limit Theorems
A Statistical Inference Framework for Coarse Data
A Related Statistical Setting
A Variational Calculus of Set Functions
Exercises

APPENDIX: BASIC CONCEPTS AND RESULTS OF PROBABILITY THEORY

References
Index
CRC Press; March 2006
268 pages; ISBN 9781420010619
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Title: An Introduction to Random Sets
Author: Hung T. Nguyen
 
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