Background
A Bayesian statistician often seeks the conditional probability distribution of a random quantity given the data. The concept of exchangeability was introduced by de Finetti. De Finetti's theorem explains a mathematical relationship between independence and exchangeability.
An infinite sequence
of random variables is said to be exchangeable if for any finite cardinal number n and any two finite sequences i1, ..., in and j1, ..., jn (with each of the is distinct, and each of the js distinct), the two sequences
both have the same joint probability distribution.
If an identically distributed sequence is independent, then the sequence is exchangeable; however, the converse is false --- there exist exchangeable random variables that are statistically dependent, for example the Polya urn model.
Read more about this topic: De Finetti's Theorem
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