Abstract: In an inference engine a conditional dependency of variables is characterized in terms of second order uncertainty to aid in improving decision making speed and precision. Mean and distribution of evidence states are utilized to provide first order uncertainties for each of a plurality of states. Higher order statistics such as standard deviation and variance for the states are calculated in order to define second order uncertainties. A covariance layer of the inference engine receives variance information from parent nodes for calculating the states of a child node. Second order uncertainty expresses conditional dependency of the parameters to which the child node responds. The method and apparatus are generalized to apply the propagation of second order uncertainty through inference engines such as Bayesian Networks, Influence Diagrams and Probabilistic Relational Models, to output control signals.