If a sequence of random variables with values in a Polish space is exchangeable (stationary) then it id conditionally i.i.d. given a random probability measure p. In the exchangeable case, two necessary and sufficient conditionas are given for the sequence to be i.i.d. given t(p). Essentially the same conditions apply when the sequence is stationary, apart from "i.i.d." is replaced by "ergodic".
On parametric models for invariant probability measures
FORTINI, SANDRA;
2000
Abstract
If a sequence of random variables with values in a Polish space is exchangeable (stationary) then it id conditionally i.i.d. given a random probability measure p. In the exchangeable case, two necessary and sufficient conditionas are given for the sequence to be i.i.d. given t(p). Essentially the same conditions apply when the sequence is stationary, apart from "i.i.d." is replaced by "ergodic".
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