On filling-in missing conditional probabilities in causal networks

Paris, J. B. (2008) On filling-in missing conditional probabilities in causal networks. [MIMS Preprint]

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Abstract

This paper considers the problem and appropriateness of filling-in missing conditional probabilities in causal networks by the use of maximum entropy. Results generalizing earlier work of Rhodes, Garside & Holmes are proved straightforwardly by the direct application of principles satisfied by the maximum entropy inference process under the assumed uniqueness of the maximum entropy solution. It is however demonstrated that the implicit assumption of uniqueness in the Rhodes, Garside & Holmes papers may fail even in the case of inverted trees. An alternative approach to filling in missing values using the limiting centre of mass inference process is then described which does not suffer this shortcoming, is trivially computationally feasible and arguably enjoys more justification in the context when the probabilities are objective (for example derived from frequencies) than by taking maximum entropy values.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Missing Information, Causal Networks, Maximum Entropy, Centre of Mass.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
Depositing User:	Ms Lucy van Russelt
Date Deposited:	06 Nov 2008
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1187

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