On representing second-order uncertainty in multi-state systems via moments of mixtures of Dirichlet distributions†
David Izraelevitz, Harry F. Martz, Deborah A Leishman, William L. Gibson · Journal of Statistical Computation and Simulation · 2009
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.