Second Order Probabilities for Uncertain and Conflicting Evidence
  In this paper the elicitation of probabilities from human 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 probabilities.
The algorithm is based on an approximate sample representation of the basic
probabilities. This sample is continuously modified by a stochastic simulation
procedure, the Metropolis algorithm, such that the sequence of successive
samples corresponds to the desired posterior distribution. The procedure is
able to combine inconsistent probabilities according to their reliability and
is applicable to general inference networks with arbitrary structure.
Dempster-Shafer probability mass functions may be included using specific
measurement distributions. The properties of the approach are demonstrated by
numerical experiments.
