De Finetti relates this particular set of exchangeable prediction rules to a Bayesian inference over a specific type of statistical model. The model that De Finetti considers comprises the so-called Bernoulli hypotheses \(h_{\theta}\), i.e., hypotheses for which  \[ P(Q^{1}_{t+1} \mid h_{\theta} \cap S_{t}) = \theta . \]  This likelihood does not depend on the string \(S_{t}\) that has gone before. The hypotheses are best thought of as determining a fixed bias \(\theta\) for the binary process, where \(\theta \in \Theta = [0, 1]\).  The representation theoremstates that there is a one-to-one mapping of priors over Bernoulli hypotheses and exchangeable prediction rules. That is, every prior distribution \(P(h_{\theta})\) can be associated with exactly one exchangeable prediction rule \(P(Q^{1}_{t+1} \mid S_{n/t})\), and conversely. Next to the original representation theorem derived by De Finetti, several other and more general representation theorems were proved, e.g., for partially exchangeable sequences and hypotheses on Markov processes (Diaconis and Freedman 1980, Skyrms 1991), for clustering predictions and partitioning processes (Kingman 1975 and 1978), and even for sequences of graphs and their generating process (Aldous 1981).