A BAYESIAN STATISTICAL-THEORY OF THE PHASE PROBLEM .1. A MULTICHANNEL MAXIMUM-ENTROPY FORMALISM FOR CONSTRUCTING GENERALIZED JOINT PROBABILITY-DISTRIBUTIONS OF STRUCTURE FACTORS
A BAYESIAN STATISTICAL-THEORY OF THE PHASE PROBLEM .1. A MULTICHANNEL MAXIMUM-ENTROPY FORMALISM FOR CONSTRUCTING GENERALIZED JOINT PROBABILITY-DISTRIBUTIONS OF STRUCTURE FACTORS
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DOI：
10.1107/s010876738800354x
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发表时间：
1988-07-01
期刊：
影响因子：
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通讯作者：
BRICOGNE, G
中科院分区：
文献类型：
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作者：
BRICOGNE, G
在这第一个完整的贝叶斯理论的晶体结构测定的三篇论文中，它表明，目前使用的所有相位信息的来源可以表示和组合通过一个通用的表达的联合概率分布的结构因素。特别注意大分子晶体学中出现的情况，其中原子的非均匀分布的适当处理是绝对必要的。一个程序，在逐步增加的复杂性的阶段，用于构建任意集合的结构因素的联合概率分布。这些结构因子可以从未知分子的一种或几种晶体形式中收集，每种晶体形式包含通过取代操作相关的一种或几种同晶结构，可能包含溶剂区域和已知片段，和/或服从一组非晶体学对称性。这个普遍的联合概率分布可以通过鞍点方法有效地近似，使用原子的最大熵分布[Bricogne（1984）。Acta Cryst. A40，410-445]和结构因子代数的推广。原子散射因子可以假定为任意的复值，因此这种形式不仅适用于X射线衍射方法，也适用于中子。这个统一的程序将在以后扩展的条件分布，允许相位扩展的建设，并能够检测和表征所有潜在来源的相位信息考虑到目前为止的似然函数，从而完成了制定一个完整的贝叶斯推理计划的晶体结构测定。
In this first of three papers on a full Bayesian theory of crystal structure determination, it is shown that all currently used sources of phase information can be represented and combined through a universal expression for the joint probability distribution of structure factors. Particular attention is given to situations arising in macromolecular crystallography, where the proper treatment of non-uniform distributions of atoms is absolutely essential. A procedure is presented, in stages of gradually increasing complexity, for constructing the joint probability distribution of an arbitrary collection of structure factors. These structure factors may be gathered from one or several crystal forms of an unknown molecule, each comprising one or several isomorphous structures related by substitution operations, possibly containing solvent regions and known fragments, and/or obeying a set of non-crystallographic symmetries. This universal joint probability distribution can be effectively approximated by the saddlepoint method, using maximum-entropy distributions of atoms [Bricogne (1984). Acta Cryst. A40, 410-445] and a generalization of structure-factor algebra. Atomic scattering factors may assume arbitrary complex values, so that this formalism applies to neutron as well as to X-ray diffraction methods. This unified procedure will later be extended by the construction of conditional distributions allowing phase extension, and of likelihood functions capable of detecting and characterizing all potential sources of phase information considered so far, thus completing the formulation of a full Bayesian inference scheme for crystal structure determination.