Hyper Normalisation and Conditioning for Discrete Probability Distributions
Abstract
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.
Cite
@article{arxiv.1607.02790,
title = {Hyper Normalisation and Conditioning for Discrete Probability Distributions},
author = {Bart Jacobs},
journal= {arXiv preprint arXiv:1607.02790},
year = {2023}
}