Hawes, Peter
(2007)
*Investigation of Properties of Some Inference Processes.*
Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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## Abstract

The spectrum of Renyi inference processes in the discrete case is found to have limits of Minimax at one end and CM∞ at the other. Another sequence of processes is found to have the limit Maximin. Although Maximin is the dual of Minimax, it is seen to have better characteristics when compared with Maximum Entropy (ME) than those possessed by Minimax. The comparison of inference processes is made using a list of desiderata which were shown by Paris/Vencovska to uniquely characterise ME. Algorithms are described for calculating Minimax and Maximin, which have the advantage over ME of inferring belief values which are rational numbers when the agent’s knowledge is itself expressed purely in terms of rational numbers. Then Minimax and Maximin are viewed as examples of Partly Linear, or PL inference processes. This yields a unique characterisation of Maximin. Another inference process, Meanimax, compares well with Minimax and is a counterexample of some plausible conjectures about certain properties of inference processes.

Item Type: | Thesis (Doctoral) |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 02 Sep 2009 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1304 |

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