exchangeability

In the subjective or personalist theory of probability a substitute must be found for the apparently objective or realist notion of an unknown probability, say of a coin coming up heads. The personalist substitute for the notion, developed by de Finetti, regards the event as a member of a sequence of tosses, which are in turn thought of as having the property that the probability of any n-fold subset of the events being a case of heads depends solely on the number n. To regard a sequence in this way is to regard events in it as exchangeable, and provides a personalist substitute for the classical notion of a sequence of independent events sharing a fixed unknown probability.