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The Three Prisoners Problem Revisited: issues in the use of Bayesian networks for security applications

By Jonathan Pickering and Zhijie Xu

Abstract

Bayesian networks are a type of causal network used\ud for probabilistic reasoning, which have found wide application in\ud biomedical environments and machine vision.We have considered\ud their application in the realm of security, where behaviour that\ud is deliberately intended to deceive has to be considered. As a\ud first step to the the analysis of this behaviour we have analysed\ud problems in which an one agent provides truthfull, but evasive,\ud information to the other agents.\ud The three prisoners problem, and its simpler relation the\ud Monty Hall problem, are classic examples of statistical analysis\ud giving rise to counter intuitive results. In this paper the source\ud of the counter intuitive results is identified as an agent that only\ud releases partial data about the true state of the system. Furthermore\ud the data that is communicated is a function of the identity\ud of the agent requesting the data. Under these circumstances two\ud significant results are demonstrated; first different questioning\ud agents, will arrive at different probability estimates for the\ud same problem. Secondly, although if all the data is requested\ud the estimated probability will converge, the convergence may\ud be nonmonotonic. This means that some questions, truthfully\ud answered, will lead to a less precise probability measurement.\ud Keywords — Bayesian reasoning; three prisoner problem

Topics: T1
Publisher: ICAC
Year: 2008
OAI identifier: oai:eprints.hud.ac.uk:4745

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Citations

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