Approximate representation of probabilistic data in expert systems

We propose the use of a third-order approximation for the representation of probabilistic data in expert systems and compare it to tree-structured representations. The differences are illustrated using the example of a reliability problem. We show that using the third-order representation results in significantly reduced losses as compared to tree structures, with a small increase in computational complexity. We present heuristic and exact techniques to determine the optimal third-order representation and propose a decomposition technique that allows the exact algorithm to be efficiently used for solving large problem instances.