Bayesian Poisson models for the graphical combination of dependent expert information

A supra-Bayesian (SB) wants to combine the information from a group of k ex perts to produce her distribution of a probability theta. Each expert gives his counts of what he thinks are the numbers of successes and failures in a sequence of independent trials, each with probability a of success. These counts, used as a surrogate for each expert's own individual probability a ssessment (together with his associated level of confidence in his estimate ), allow the SE to build various plausible conjugate models. Such models re flect her beliefs about the reliability of different experts and take accou nt of different possible patterns of overlap of information between them. C orresponding combination rules are then obtained and compared with other mo re established rules and their properties examined.