一句话：将概率正规化从偏函数重构为输出分布之分布的全函数，并用于条件化与定量信息流 refinement。
概率论中的正规化把次分布变为真分布，但对零次分布无定义，因而是一个偏操作，给等式推理带来困难。本文为离散概率分布提出一种新的“Hyper”正规化描述，将其定义为行为良好的全函数；其输出是分布之上的分布。作者先建立这一（Hyper）正规化理论的基本性质，随后用它给出条件化的新描述，产生条件分布之上的分布。该框架改善了关于正规化的等式推理，并给出定量信息流中 refinement 的一种清晰抽象重述。
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description of normalisation is given as a mathematically well-behaved total function. The output of this `hyper' normalisation operation is a distribution of distributions. It improves reasoning about normalisation. After developing the basics of this theory of (hyper) normalisation, it is put to use in a similarly new description of conditioning, producing a distribution of conditional distributions. This is used to give a clean abstract reformulation of refinement in quantitative information flow.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{000117a,
title = {Hyper Normalisation and Conditioning for Discrete Probability Distributions},
author = {Bart Jacobs},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 3},
year = {2017},
doi = {10.23638/lmcs-13(3:17)2017}
}