## Epsilon-Exchangeability?

February 12, 2010

Eventually here, I want to share some thoughts and a question that I have had lately pertaining to de Finetti’s notion of exchangeability. First, however, I want to set the stage for these thoughts by providing some background. If you are already informed on the basic points pertaining to de Finetti’s representation theorem and its epistemological implications, you will probably just want to skip right to the section on “$\epsilon$-exchangeability?”.

Background

De Finetti defines exchangeability as follows (p. 123*):

$X_1,X_2,...,X_n,...$ are exchangeable random quantities if they play a symmetrical role in relation to all problems of probability, or, in other words, if the probability that $X_{i_1},X_{i_2},...,X_{i_n}$ satisfy a given condition is always the same however the distinct indices $i_1...i_n$ are chosen.