Jacobs, Bart - Hyper Normalisation and Conditioning for Discrete Probability Distributions

lmcs:3885 - Logical Methods in Computer Science, August 29, 2017, Volume 13, Issue 3
Hyper Normalisation and Conditioning for Discrete Probability Distributions

Authors: Jacobs, Bart

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.


Source : oai:arXiv.org:1607.02790
DOI : 10.23638/LMCS-13(3:17)2017
Volume: Volume 13, Issue 3
Published on: August 29, 2017
Submitted on: August 29, 2017
Keywords: Computer Science - Logic in Computer Science,18C10,F.1.2,I.2.3


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