Uncertainty analysis in Bayesian networks

Abstract

Most parameter probabilities of a Bayesian network which are assessed by domain experts include at least some form of inaccuracy. To study the (joint) effect that inaccuracies in one or multiple parameter probabilities of a Bayesian network has on a probability of interest, a sensitivity analysis or an uncertainty analysis can be performed. A sensitivity analysis has a high computational cost in comparison to the computational cost of an uncertainty analysis and its result is difficult to interpret. Due to the high computational cost of performing a sensitivity analysis it has been suggested to instead perform an uncertainty analysis. An uncertainty analysis takes a sampling approach, in each sample step, the parameter probability values under study are drawn from an associated pre-specified sampling distribution and the probability of interest is computed and recorded. The result of an uncertainty analysis reveals a distribution of the recorded output values without any explicit reference to parameter probability values. There is however little experience in how to perform an uncertainty analysis and little insight in how to interpret its result. In this thesis, we gain more insight on how to interpret the result of an uncertainty analysis in terms of how inaccuracies in parameter probabilities of a Bayesian network affect a probability of interest. The beta distribution is chosen as sampling distribution to represent the uncertainty in the parameter probability values. Our analytical results showed that predictions about the results of a uncertainty analysis can be made when using the beta distribution as sampling distribution. In our experiment, a number of uncertainty analyses were performed three times, each time a different method was used to represent the uncertainty in the parameter probability values. The methods used different prior knowledge about the parameter probability value, as elicited from a domain experts, for representing the uncertainty in the parameter probability values. The experimental findings provided insights in how to interpret the result of an uncertainty analysis in terms of how inaccuracies in parameter probabilities of a Bayesian network affect a probability of interest. Further is shown that the result of an uncertainty analysis, where the joint effect that inaccuracies in 3 or more parameter probabilities of a Bayesian network has on a probability of interest is studied, is hard to interpret since the result has no reference to the parameter probability values.