A Bayesian statistical theory of the phase problem. I. A multichannel maximum-entropy formalism for constructing generalized joint probability distributions of structure factors

摘要: In this first of three papers on a full Bayesian theory crystal structure determination, it is shown that all currently used sources phase information can be represented and combined through universal expression for the joint probability distribution factors. Particular attention given to situations arising in macromolecular crystallography, where proper treatment non-uniform distributions atoms absolutely essential. A procedure presented, stages gradually increasing complexity, constructing an arbitrary collection These factors may gathered from one or several forms unknown molecule, each comprising isomorphous structures related by substitution operations, possibly containing solvent regions known fragments, and/or obeying set non-crystallographic symmetries. This effectively approximated saddlepoint method, using maximum-entropy [Bricogne (1984). Acta Cryst. A40, 410-445] generalization structure-factor algebra. Atomic scattering assume complex values, so formalism applies neutron as well X-ray diffraction methods. unified will later extended construction conditional allowing extension, likelihood functions capable detecting characterizing potential considered far, thus completing formulation inference scheme determination.