De Finetti's representation theorem relates rules for prediction, as functions of the given sample data, to Bayesian statistical analyses of those data, against the background of a statistical model. See Festa (1996) and Suppes (2001) for useful introductions. De Finetti considers a process that generates a series of time-indexed observations, and he then studies prediction rules that take these finite segments as input and return a probability over future events, using a statistical model that can analyze such samples and provide the predictions. The key result of De Finetti is that a particular statistical model, namely the set of all distributions in which the observations are independently and identically distributed, can be equated with the class of exchangeable prediction rules, namely the rules whose predictions do not depend on the order in which the observations come in.