Molchanov, Ilya (2004). Applications of random sets in image analysis. How to average a cat and a dog? In: Soft methodology and random information systems. Advances in intelligent and soft computing: Vol. 26 (pp. 8-18). Berlin: Springer
Full text not available from this repository.The expectation (or average) is one of the basic concepts in probability theory and statistical inference. However, this rather basic concept becomes fairly complicated for random elements in non-linear spaces. The family of compact sets is a typical example of such non-linear space, alongside with numerous possible examples that involve curved spaces. To highlight various complications, it is possible to consider a random compact set that with equal probabilities is the unit interval or its end-points, or a set that is either the circle or the disk bounded by it, or a set that takes values {0} or {0, 1}. Various definitions of expectations respect the shape of the set, its cardinality or measure, or its connectivity properties.
Item Type: |
Book Section (Review Article) |
---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Molchanov, Ilya |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1867-5662 |
ISBN: |
978-3-540-44465-7 |
Series: |
Advances in intelligent and soft computing |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Ilya Molchanov |
Date Deposited: |
19 Aug 2016 08:03 |
Last Modified: |
05 Dec 2022 14:57 |
URI: |
https://boris.unibe.ch/id/eprint/85367 |