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Imprecise Bernoulli processes

Jasper De Bock UGent and Gert De Cooman UGent (2012) Communications in Computer and Information Science. 299(4). p.400-409
abstract
In classical Bernoulli processes, it is assumed that a single Bernoulli experiment can be described by a precise and precisely known probability distribution. However, both of these assumptions can be relaxed. A first approach, often used in sensitivity analysis, is to drop only the second assumption: one assumes the existence of a precise distribution, but has insufficient resources to determine it precisely. The resulting imprecise Bernoulli process is the lower envelope of a set of precise Bernoulli processes. An alternative approach is to drop both assumptions, meaning that we don't assume the existence of a precise probability distribution and regard the experiment as inherently imprecise. In that case, a single imprecise Bernoulli experiment can be described by a set of desirable gambles. We show how this set can be extended to describe an imprecise Bernoulli process, by imposing the behavioral assessments of epistemic independence and exchangeability. The resulting analysis leads to surprisingly simple mathematical expressions characterizing this process, which turn out to be the same as the ones obtained through the straightforward sensitivity analysis approach.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
IID processes, nomials, Bernstein poly, sensitivity analysis, exchangeability, imprecise Bernoulli processes, temic independence, epis, exchangeably independent natural extension, sets of desirable gambles
in
Communications in Computer and Information Science
Commun. comput. inf. sci.
volume
299
issue
4
issue title
Advances in computational intelligence
pages
400 - 409
publisher
Springer
place of publication
Berlin, Germany
conference name
14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU - 2012)
conference location
Catania, Italy
conference start
2012-07-09
conference end
2012-07-13
ISSN
1865-0929
DOI
10.1007/978-3-642-31718-7_42
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2082289
handle
http://hdl.handle.net/1854/LU-2082289
date created
2012-04-06 16:09:14
date last changed
2012-08-08 09:44:39
@inproceedings{2082289,
  abstract     = {In classical Bernoulli processes, it is assumed that a single Bernoulli experiment can be described by a precise and precisely known probability distribution. However, both of these assumptions can be relaxed. A first approach, often used in sensitivity analysis, is to drop only the second assumption: one assumes the existence of a precise distribution, but has insufficient resources to determine it precisely. The resulting imprecise Bernoulli process is the lower envelope of a set of precise Bernoulli processes. An alternative approach is to drop both assumptions, meaning that we don't assume the existence of a precise probability distribution and regard the experiment as inherently imprecise. In that case, a single imprecise Bernoulli experiment can be described by a set of desirable gambles. We show how this set can be extended to describe an imprecise Bernoulli process, by imposing the behavioral assessments of epistemic independence and exchangeability. The resulting analysis leads to surprisingly simple mathematical expressions characterizing this process, which turn out to be the same as the ones obtained through the straightforward sensitivity analysis approach.},
  author       = {De Bock, Jasper and De Cooman, Gert},
  booktitle    = {Communications in Computer and Information Science},
  issn         = {1865-0929},
  keyword      = {IID processes,nomials,Bernstein poly,sensitivity analysis,exchangeability,imprecise Bernoulli processes,temic independence,epis,exchangeably independent natural extension,sets of desirable gambles},
  language     = {eng},
  location     = {Catania, Italy},
  number       = {4},
  pages        = {400--409},
  publisher    = {Springer},
  title        = {Imprecise Bernoulli processes},
  url          = {http://dx.doi.org/10.1007/978-3-642-31718-7\_42},
  volume       = {299},
  year         = {2012},
}

Chicago
De Bock, Jasper, and Gert De Cooman. 2012. “Imprecise Bernoulli Processes.” In Communications in Computer and Information Science, 299:400–409. Berlin, Germany: Springer.
APA
De Bock, Jasper, & De Cooman, G. (2012). Imprecise Bernoulli processes. Communications in Computer and Information Science (Vol. 299, pp. 400–409). Presented at the 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU - 2012), Berlin, Germany: Springer.
Vancouver
1.
De Bock J, De Cooman G. Imprecise Bernoulli processes. Communications in Computer and Information Science. Berlin, Germany: Springer; 2012. p. 400–9.
MLA
De Bock, Jasper, and Gert De Cooman. “Imprecise Bernoulli Processes.” Communications in Computer and Information Science. Vol. 299. Berlin, Germany: Springer, 2012. 400–409. Print.