Probabilistic connexion between one phase invariant and moduli of all structure factors

Recalling the `conditional joint probability law' of m normalized structure factors [Tsoucaris (1969), C.R. Acad. Sci. Paris, Sér. B, 268, 875; (1970). Acta Cryst. A26, 492] the conditional probability density is established for three moduli, assuming that the structure invariant α is known. Then, using the Bayes theorem, in order to `invert' the role of random variables and known parameters, the probability density of α is obtained under the condition that the moduli are fixed. By the application of the axiom of joint probabilities for vectors running over all reciprocal lattice points located within the observable Ewald sphere, the expression for one phase invariant α is derived as a function of all observed moduli p(α|all moduli).