Evaluating crystallographic likelihood functions using numerical quadratures

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 targets functions. Here a numerical quadrature is developed that allows for the rapid evaluation of intensity-based likelihood functions in crystallographic applications. By using a sequence of change of variable transformations, including a non-linear domain compression operation, an accurate, robust, and efficient quadrature is constructed. The approach is flexible and can incorporate different noise models with relative ease.