Abstract
| Lingua originale | English |
|---|---|
| Titolo della pubblicazione ospite | Symbolic and Quantitative Approaches to Reasoning with Uncertainty |
| Pagine | 218-229 |
| Numero di pagine | 12 |
| Stato di pubblicazione | Published - 2013 |
Serie di pubblicazioni
| Nome | LECTURE NOTES IN COMPUTER SCIENCE |
|---|
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All Science Journal Classification (ASJC) codes
- Computer Science(all)
- Theoretical Computer Science
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Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence. / Sanfilippo, Giuseppe; Gilio, Angelo.
Symbolic and Quantitative Approaches to Reasoning with Uncertainty. 2013. pag. 218-229 (LECTURE NOTES IN COMPUTER SCIENCE).Risultato della ricerca: Chapter
}
TY - CHAP
T1 - Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence
AU - Sanfilippo, Giuseppe
AU - Gilio, Angelo
PY - 2013
Y1 - 2013
N2 - We consider conditional random quantities (c.r.q.’s) in the setting of coherence. Given a numerical r.q. X and a non impossible event H, based on betting scheme we represent the c.r.q. X|H as the unconditional r.q. XH + μH c , where μ is the prevision assessed for X|H. We develop some elements for an algebra of c.r.q.’s, by giving a condition under which two c.r.q.’s X|H and Y|K coincide. We show that X|HK coincides with a suitable c.r.q. Y|K and we apply this representation to Bayesian updating of probabilities, by also deepening some aspects of Bayes’ formula. Then, we introduce a notion of iterated c.r.q. (X|H)|K, by analyzing its relationship with X|HK. Our notion of iterated conditional cannot formalize Bayesian updating but has an economic rationale. Finally, we define the coherence for prevision assessments on iterated c.r.q.’s and we give an illustrative example.
AB - We consider conditional random quantities (c.r.q.’s) in the setting of coherence. Given a numerical r.q. X and a non impossible event H, based on betting scheme we represent the c.r.q. X|H as the unconditional r.q. XH + μH c , where μ is the prevision assessed for X|H. We develop some elements for an algebra of c.r.q.’s, by giving a condition under which two c.r.q.’s X|H and Y|K coincide. We show that X|HK coincides with a suitable c.r.q. Y|K and we apply this representation to Bayesian updating of probabilities, by also deepening some aspects of Bayes’ formula. Then, we introduce a notion of iterated c.r.q. (X|H)|K, by analyzing its relationship with X|HK. Our notion of iterated conditional cannot formalize Bayesian updating but has an economic rationale. Finally, we define the coherence for prevision assessments on iterated c.r.q.’s and we give an illustrative example.
KW - Coherence, betting scheme, conditional random quantities, conditional previsions, Bayesian updating, iterated conditioning.
UR - http://hdl.handle.net/10447/97510
UR - http://link.springer.com/chapter/10.1007%2F978-3-642-39091-3_19
M3 - Chapter
SN - 978-3-642-39090-6
T3 - LECTURE NOTES IN COMPUTER SCIENCE
SP - 218
EP - 229
BT - Symbolic and Quantitative Approaches to Reasoning with Uncertainty
ER -