Co-variation for sensitivity analysis in Bayesian networks: Properties, consequences and alternatives

• Sensitivity analysis in Bayesian networks assumes proportional co-variation of parameters.
• Alternative co-variation schemes with interesting properties can be defined.
• Sensitivity functions retain their general form under linear schemes.
• CD-distance computations can incorporate different co-variation schemes.

Upon varying parameters in a sensitivity analysis of a Bayesian network, the standard approach is to co-vary the parameters from the same conditional distribution such that their proportions remain the same. Alternative co-variation schemes are, however, possible. In this paper we investigate the properties of the standard proportional co-variation and introduce two alternative schemes: uniform and order-preserving co-variation. We theoretically investigate the effects of using alternative co-variation schemes on the so-called sensitivity function, and conclude that its general form remains the same under any linear co-variation scheme. In addition, we generalise the CD-distance for bounding global belief change to explicitly include the co-variation scheme under consideration. We prove a tight lower bound on this distance for parameter changes in single conditional probability tables.