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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.

Acta Crystallographica. Section D, Structural Biology
|August 4, 2020
PubMed
Summary
This summary is machine-generated.

A new numerical method rapidly computes intensity-based likelihood functions for crystallography. This advance improves structural analysis from limited diffraction data, enhancing crystallographic applications.

Keywords:
maximum likelihoodnumerical integrationrefinement

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Area of Science:

  • Crystallography
  • Computational Chemistry
  • Data Analysis

Background:

  • Intensity-based likelihood functions can improve crystallographic structure quality, especially with limited diffraction data.
  • Efficient computation of these functions is a significant challenge in crystallographic applications.

Purpose of the Study:

  • To develop a numerical quadrature for rapid evaluation of intensity-based likelihood functions.
  • To enhance the usability of these functions in crystallographic structure determination.

Main Methods:

  • A numerical quadrature is developed using a sequence of change-of-variable transformations.
  • A nonlinear domain-compression operation is employed for robust and efficient computation.
  • The method is designed for flexibility to incorporate various noise models.

Main Results:

  • The developed quadrature allows for rapid and accurate evaluation of intensity-based likelihood functions.
  • The approach is robust and efficient, overcoming previous computational limitations.
  • The method demonstrates flexibility in handling different noise models.

Conclusions:

  • The numerical quadrature provides an efficient and accurate solution for computing intensity-based likelihood functions in crystallography.
  • This method facilitates the use of these functions, potentially improving crystallographic structure quality from marginal diffraction data.