Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence

Giuseppe Sanfilippo, Angelo Gilio

Risultato della ricerca: Chapter

14 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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    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).