Second order probabilities for uncertain and conflicting evidence

1988; Lauritzen & Spiegelhalter 1988) cannot work as there extsts no probability measure that In this paper the elicitation of probabilities from simultaneously meets all constraints. The ratiohuman experts is considered as a measurement process, which may be disturbed by random ·measurement noise'. Using Bayesian concepts a second order probability distribution is derived reflecting the uncertainty of the input probabil­ Ities. The algorithm is based on an approxi­ mate sample representation of the basic proba­ bilities. This sample is continuously modified by a stochastic simulation procedure. the Metropo­ lis algorithm, such that the sequence of succes­ sive samples corresponds to the desired posterior distribution. The procedure is able to combine inconsistent probabilities according to their re­ liability and is applicable to general inference networks with arbitrary structure. Dempster­ Shafer probability mass functions may be in­ cluded using specific measurement distributions. The properties of the approach are demonstrated by numerical experiments.