Conditional external Bayesianity in decomposable influence diagrams

Faria, Álvaro E. and Smith, Jim Q. (1996). Conditional external Bayesianity in decomposable influence diagrams. In: Bernardo, J. M.; Berger, J. O.; Dawid, A. P. and Smith, A. F. M. eds. Bayesian Statistics 5: Proceedings of the Fifth Valencia International Meeting, June 5-9, 1994. Oxford: Clarendon Press, pp. 551–560.



This paper addresses the group decision problem, where the members of a group may be jointly responsible for a decision. We shall assume that the group has agreed on the structure of associations of variables in a problem, as might be represented by a commonly agreed influence diagram (ID). However, the members of that group diverge about the actual conditional probability distributions for the variables in that ID. The algorithm we suggest they adopt is one which demands, at least on learning information which preserves the ID structure, that the pool of conditional. distributions associated with the ID are externally Bayesian (EB). It is illustrated why such a generalisation of external Bayesianity is practically quite useful.

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