Talk:Exchangeable random variables

I created this article from WP:AFC upon request from 141.250.5.8 09:32, 29 August 2006 (UTC). I'm not an expert on statistics or probability theory, so I may have miscategorized the article or whatever. Feel free to correct it. --Elkman - (Elkspeak) 18:53, 29 August 2006 (UTC)

I think it would be better to have an article on exchangeable random variables that would include a definition of exchangeability of events as a special case. I'll be back.... Michael Hardy 16:33, 24 June 2007 (UTC)

What does the last sentence in the first paragraph actually mean? Is it supposed to say that the future random variables are unpredictable from the past ones? —Preceding unsigned comment added by 86.3.188.231 (talk) 13:34, 20 January 2011 (UTC)

No it is not supposed to be saying that, rather the opposite. There is useful information for prediction in "past" or "other" observations, although the context in which exchangeability is used is never particularly related to this. The examples are rather poor and a perhaps easier one is the following" suppose there is a single rv Y and several independent (iid) rv's Z, and define

$X_{i}=Y+Z_{i}.$

Then the collection of X_i are dependent, because of the common Y, but exchangeable. The dependence means that the conditional distribution of some of the X_i given others is different from the marginal distribution ... hence knowing some of the X values can be used to predict others, better than not knowing those X values. It will probably be better to entirely replace the first paragraph with something that means something. Melcombe (talk) 10:00, 21 January 2011 (UTC)

Characterization is sloppy

In statistics, an exchangeable sequence of random variables (also sometimes interchangeable)[1] is a sequence such that future observations behave like earlier observations, meaning formally that any order (of a finite number of observations) is equally likely. This formalizes the notion of "the future being predictable on the basis of past experience."

I disagree. This is a mischaracterization. Exchangeability is a kind of homogeneity or symmetry, sure, but to tie it specifically to the notion of predicting the future from the past is to read too much into it. Then any kind of similarity of anything to anything is tied to predicting the future from the past. For example, the concept of i.i.d. would be tied to it. 178.38.132.48 (talk) 21:34, 2 December 2017 (UTC)

No Cesaro sum

In the part about the representation theorem the author suddenly speaks about the Cesaro limit of indicator functions. However, this is no Cesaro sum at all, it merely the limit of partial sums. Nmdwolf (talk)