APPLICATION OF BAYES THEOREM WHEN TRUE DATA STATE IS UNCERTAIN

This paper discusses the application of Bayes's theorem to those cases where the true state of the world is not known with certainty. An algorithm is proposed that relaxes the requirement of Bayes's theorem that the true data state be known with certainty by postulating a true but unobservable elementary event, ω, which gives rise to posterior probabilities which reflect the uncertainty of the data. A derivation is presented for the calculation of Bayesian posterior probabilities which uses as its input these probabilities, rather than the true event, ω, which is assumed to be unavailable. Suggestions are made as to the application of this modification of Bayes's theorem to cascaded inference processes. © 1969.