Finite partial exchangeability (Q803640)

In this pithy paper the author gives concise proofs of previous results of de Finetti, Diaconis and Jaynes, according to which infinite exchangeability implies non-negative correlation, and to the marginalizability condition of a 2-dimensional exchangeable distribution. The results are then generalized to partial exchangeability with simple events from two classes. First an inequality is given which characterizes the case of infinite partial exchangeability (Theorem 3). The marginalizability condition (Theorem 4) for a \(2\times 2\)-event partially exchangeable sequence is that \(AH\geq D^ 2\), with A the probability of two successes in the first class, H the similarity for the second, and D one success in each class, in two trials.