Maximum Entropy and Bayesian Statistics in Crystallography: a Review of Practical Applications

A survey of practical applications of the maximum entropy method to problems in crystallography is presented along with the related field of Bayesian statistical inference. Included in this review are problems of the processing of intensity data, the crystallographic phase problem, accurate electron-density studies and algorithms for the constrained maximization of entropy. The discussion of the phase problem reviews the solution of structures from powder and single-crystal diffraction data sets, as well as applications to electron and macromolecular crystallography. It is believed that the methodology has a secure future and a sound statistical basis, but it is still not a technique that is regularly employed by crystallographers and the reasons for this are also examined.