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首页> 外文期刊>Acta crystallographica. Section D, Structural biology >On the suitability of using the diagonal Gaussian approximation in the calculation of the magnitude-based likelihood function
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On the suitability of using the diagonal Gaussian approximation in the calculation of the magnitude-based likelihood function

机译：使用斜高斯的适用性近似的计算magnitude-based似然函数

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摘要

Statistical likelihood maximization is currently one of the main tools in computational procedures in biological crystallography. In these procedures, the likelihood function is calculated, as a rule, within the framework of a diagonal Gaussian approximation (DGA) of the joint probability distribution of the real and imaginary parts of a set of structure factors. This approximation assumes pairwise uncorrelated values of various structure-factor components. In this paper, exact formulas are derived for pairwise correlations of structure factors, and conditions under which these correlations can be considered to be negligible are discussed. It is shown that in the case where the probability distribution of the atomic coordinates is related to the region of the molecule or its domains, the correlation of the structure factors of reflections s and w is determined mostly by the magnitudes of the Fourier transform of the probability distribution calculated at the points 2s, 2w, s — w and s + w. However, in the case where the probability distribution describes small corrections to the coordinates of the existing preliminary atomic model, the correlation is determined by the values of the structure factors of the preliminary model that correspond to the 2s, 2w, s — w and s + w reflections rather than by the Fourier transform of the probability distribution. Test cases demonstrate that the practice of using the DGA for calculation of the likelihood when based on sets containing neighbouring reflections may be unjustified in some crystallographic applications, especially in single-particle studies.
机译：统计目前可能性最大化计算程序的主要工具之一在生物晶体学。程序,似然函数计算规则的框架内斜高斯近似(DGA)的联合概率分布的真实虚部的一组结构的因素。这个近似假设两两不相关的各种结构因子组件的值。本文的公式推导两两相互关系的结构因素,这些相关性的条件下被认为是可以忽略的。显示的情况下的概率原子坐标的分布有关该地区的分子或其领域,相关的结构因素反射和w是主要的决定的傅里叶变换的大小概率分布计算的点2 s, 2 w s - w和s + w。然而,在这个案子概率分布描述了在哪里小修正的坐标现有的初步原子模型相关的值决定结构因素的初步模型对应的2 s, 2 w s - w和s + w反射而不是通过傅里叶变换的概率分布。证明使用DGA的做法当基于计算的可能性集包含邻近的倒影不正当的在某些晶体应用程序,特别是在单粒子研究。

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