Hyper Normalisation and Conditioning for Discrete Probability Distributions
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 mathemat...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2017-08-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/2009/pdf |
| _version_ | 1797268624256270336 |
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| author | Bart Jacobs |
| author_facet | Bart Jacobs |
| author_sort | Bart Jacobs |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T01:35:26Z |
| format | Article |
| id | doaj.art-51f2a23548154c1bbaf0f69615d4e272 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:26Z |
| publishDate | 2017-08-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-51f2a23548154c1bbaf0f69615d4e2722024-03-08T09:51:11ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742017-08-01Volume 13, Issue 310.23638/LMCS-13(3:17)20172009Hyper Normalisation and Conditioning for Discrete Probability DistributionsBart JacobsNormalisation 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.https://lmcs.episciences.org/2009/pdfcomputer science - logic in computer science18c10f.1.2i.2.3 |
| spellingShingle | Bart Jacobs Hyper Normalisation and Conditioning for Discrete Probability Distributions Logical Methods in Computer Science computer science - logic in computer science 18c10 f.1.2 i.2.3 |
| title | Hyper Normalisation and Conditioning for Discrete Probability Distributions |
| title_full | Hyper Normalisation and Conditioning for Discrete Probability Distributions |
| title_fullStr | Hyper Normalisation and Conditioning for Discrete Probability Distributions |
| title_full_unstemmed | Hyper Normalisation and Conditioning for Discrete Probability Distributions |
| title_short | Hyper Normalisation and Conditioning for Discrete Probability Distributions |
| title_sort | hyper normalisation and conditioning for discrete probability distributions |
| topic | computer science - logic in computer science 18c10 f.1.2 i.2.3 |
| url | https://lmcs.episciences.org/2009/pdf |
| work_keys_str_mv | AT bartjacobs hypernormalisationandconditioningfordiscreteprobabilitydistributions |