The joint probability distribution of any set of phases given any set of diffraction magnitudes. I. Theoretical considerations

Conditional joint probability distribution functions P(φ₁, ..., φ_n| R₁, ..., R_n, ..., R_p) of any set of n phases given any set of p diffraction moduli are calculated. The distributions include terms up to order 1/N and involve both triplet and quartet contributions. Two types of formulae are derived, which may be considered as developments of two mathematical approaches described by Hauptman [Acta Cryst. (1975). A31, 680–687] and by Giacovazzo [Acta Cryst. (1975). A31, 252–259; Acta Cryst. (1976). A32, 91–99] for the estimation of the quartet invariants.