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Imprecise Bernoulli processes

Jasper De Bock UGent (2012) SYSTeMS Dialogue, Presentations.
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
in
SYSTeMS Dialogue, Presentations
conference name
SYSTeMS Dialogue
conference location
Ghent, Belgium
conference start
2012-04-26
conference end
2012-04-26
language
English
UGent publication?
yes
classification
C3
copyright statement
I have retained and own the full copyright for this publication
id
2107023
handle
http://hdl.handle.net/1854/LU-2107023
date created
2012-05-15 12:13:25
date last changed
2012-05-16 13:09:31
@inproceedings{2107023,
  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},
  booktitle    = {SYSTeMS Dialogue, Presentations},
  language     = {eng},
  location     = {Ghent, Belgium},
  title        = {Imprecise Bernoulli processes},
  year         = {2012},
}

Chicago
De Bock, Jasper. 2012. “Imprecise Bernoulli Processes.” In SYSTeMS Dialogue, Presentations.
APA
De Bock, Jasper. (2012). Imprecise Bernoulli processes. SYSTeMS Dialogue, Presentations. Presented at the SYSTeMS Dialogue.
Vancouver
1.
De Bock J. Imprecise Bernoulli processes. SYSTeMS Dialogue, Presentations. 2012.
MLA
De Bock, Jasper. “Imprecise Bernoulli Processes.” SYSTeMS Dialogue, Presentations. 2012. Print.