ON REPRESENTING SECOND-ORDER UNCERTAINTY IN MULTI-STATE SYSTEMS VIA MOMENTS OF MIXTURES OF DIRICHLET DISTRIBUTIONS

Second-order probabilities have been proposed as representations of the uncertainty in the parameters of probabilistic models such as Bayesian belief networks. We investigate conditions under which second-order probabilities can be represented in terms of their marginal moments. We show that certain combinations of marginal means and variances do not correspond to any valid second-order joint distribution. By fitting a Dirichlet mixture to marginal mean and variance information, we derive sufficient conditions for a valid second-order joint distribution to exist. †LA-UR-07-1330