272 Pages
1 B/W Illustrations
by
Chapman & Hall
268 Pages
1 B/W Illustrations
by
Chapman & Hall
272 Pages
by
Chapman & Hall
Also available as eBook on:
The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that in science and engineering, and even in the... Read more
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
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
Biography
Nguyen, Hung T.
