Paper Info
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+μHc, 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.
Year
DOI
Venue
2013
10.1007/978-3-642-39091-3_19
ECSQARU
Keywords
Field
DocType
suitable c,conditional random quantity,illustrative example,unconditional r,numerical r,iterated c,prevision assessment,economic rationale,formalize bayesian,iterated conditioning,non impossible event h
Discrete mathematics,Bayesian inference,Conditioning,Coherence (physics),Iterated function,Mathematics,Bayes' theorem
Conference
Citations 
PageRank 
References 
9
0.69
23
Authors
2
Name
Order
Citations
PageRank
Angelo Gilio141942.04
Giuseppe Sanfilippo220417.14