Uncertain evidence and nonlocality

After the work of Suppes and Zanotti it is clear that the proof of the impossibility of local theories is a probability argument. The notion of locality is essentially a principle of conditional statistical independence which is strictly tied to that of exchangeability. De Finetti's celebrated representation theorem makes the connection clear. The way in which Bell's experiment is performed suggests that the probability function which is more suitable to describe it is not exchangeable, but partially exchangeable. It is known that partially exchangeable probability functions show a nonlocal behavior. Working with these functions, it is possible to make use of observations regarding one stochastic process in order to change the distribution of another process. We enlarge to uncertain evidence a classical probability function we have used in deriving some quantum correlations. By means of this enlargement we give simple examples of a nonlocal probability function.