Bayes reliability estimation using multiple sources of prior information: binomial sampling

The authors develop Bayes estimators for the true binomial survival probability when there exist multiple sources of prior information. For each source of prior information, incomplete (partial) prior information is assumed to exist in the form of either a stated prior mean of p or a stated prior credibility interval on p; p is the parameter about which there is a degree of belief regarding its unknown value, i.e., p is treated as though it were the unknown value of a random variable. Both maximum entropy and maximum posterior risk criteria are used to determine a beta prior for each source. A mixture of these beta priors is then taken as the combined prior, after which Bayes theorem is used to obtain the final mixed beta posterior distribution from which the desired estimates are obtained. Two numerical examples illustrate the method