Incorporation of prior phase information strengthens maximum-likelihood structure refinement

The application of a maximum-likelihood analysis to the problem of structur e refinement has led to striking improvements over the traditional least-sq uares methods. Since the method of maximum likelihood allows for a rational incorporation of other sources of information, we have derived a likelihoo d function that incorporates experimentally determined phase information. I n a number of different test cases, this target function performs better th an either a least-squares target or a maximum-likelihood function lacking p rior phases. Furthermore, this target gives significantly better results co mpared with other functions incorporating phase information. When combined with a procedure to mask 'unexplained' density, the phased likelihood targe t also makes it possible to refine very incomplete models.