Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence

Giuseppe Sanfilippo, Angelo Gilio

Risultato della ricerca: Chapter

13 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteSymbolic and Quantitative Approaches to Reasoning with Uncertainty
Pagine218-229
Numero di pagine12
Stato di pubblicazionePublished - 2013

Serie di pubblicazioni

NomeLECTURE NOTES IN COMPUTER SCIENCE

Fingerprint

Conditioning
Bayesian Updating
Algebra
Economics
Bayes' Formula

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Theoretical Computer Science

Cita questo

Sanfilippo, G., & Gilio, A. (2013). Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty (pagg. 218-229). (LECTURE NOTES IN COMPUTER SCIENCE).

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

Sanfilippo, G & Gilio, A 2013, Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence. in Symbolic and Quantitative Approaches to Reasoning with Uncertainty. LECTURE NOTES IN COMPUTER SCIENCE, pagg. 218-229.
Sanfilippo G, Gilio A. Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty. 2013. pag. 218-229. (LECTURE NOTES IN COMPUTER SCIENCE).
Sanfilippo, Giuseppe ; Gilio, Angelo. / Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence. Symbolic and Quantitative Approaches to Reasoning with Uncertainty. 2013. pagg. 218-229 (LECTURE NOTES IN COMPUTER SCIENCE).
@inbook{c96527960df848ddad51e653545577ef,
title = "Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence",
abstract = "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.",
keywords = "Coherence, betting scheme, conditional random quantities, conditional previsions, Bayesian updating, iterated conditioning.",
author = "Giuseppe Sanfilippo and Angelo Gilio",
year = "2013",
language = "English",
isbn = "978-3-642-39090-6",
series = "LECTURE NOTES IN COMPUTER SCIENCE",
pages = "218--229",
booktitle = "Symbolic and Quantitative Approaches to Reasoning with Uncertainty",

}

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 -