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Evaluating crystallographic likelihood functions using numerical quadratures
Petrus H Zwart1, Elliott D Perryman1
1Center for Advanced Mathematics in Energy Research Applications, Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA.
Abstract:
Intensity-based likelihood functions in crystallographic applications have the potential to enhance the quality of structures derived from marginal diffraction data. Their usage, however, is complicated by the ability to efficiently compute these target functions. Here, a numerical quadrature is developed that allows the rapid evaluation of intensity-based likelihood functions in crystallographic applications. By using a sequence of change-of-variable transformations, including a nonlinear domain-compression operation, an accurate, robust and efficient quadrature is constructed. The approach is flexible and can incorporate different noise models with relative ease.
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