Exchangeability and Conditionally Identical Common Cause Systems |
| |
| Authors: | Gábor Hofer-Szabó |
| |
| Institution: | (1) Department of Philosophy and History of Science, Budapest University of Technology and Economics, Budapest, Hungary;(2) Cambridge University Press, Cambridge, USA |
| |
| Abstract: | A pair (A, B) of events in a classical probability measure space (Ω, p) is called exchangeable iff p(A
 ) = p(
B). Conditionally identical common cause system of size n for the correlation is an n-partition of Ω such that (i) any member of the partition screens the correlation off and (ii) for any member {C
i
}
i ∊ I
of the partition p(A|C
i
) = p(B|C
i
). The common cause system is called proper if p(A|C
i
)≠(A|C
j
) for some i ≠ j. In the paper it is shown that exchangeable correlations be explained by proper conditionally identical common cause systems in the following sense. (i) Given a proper conditionally identical common cause system of size n for the two events A and B in Ω, then the pair (A, B) will be an exchangeable (positively) correlating pair. (ii) Given any exchangeable (positively) correlating pair of events in Ω and given any finite number n > 2, then the probability space can be embedded into a larger probability space in such a way that the larger space contains a proper conditionally identical common cause system of size n for the correlation. |
| |
| Keywords: | Reichenbachian common cause exchangeability correlation |
| 本文献已被 SpringerLink 等数据库收录！ |
|
