The process of building a Bayesian network model is often a bottleneck in applying the Bayesian network approach to real-world problems. One of the daunting tasks is the quantification of the Bayesian network that often requires specifying a huge number of conditional probabilities. On the other hand, the sensitivity of the network’s performance to variations in different probability parameters may be quite different; thus, certain parameters should be specified with a higher precision than the others. We present a method for a selective update of the probabilities based on the results of sensitivity analysis performed during learning a Bayesian network from data. We first perform the sensitivity analysis on a Bayesian network in order to identify the most important (most critical) probability parameters, and then further update those probabilities to more accurate values. The process is repeated until refining the probabilities any further does not improve the performance of the network. Our method can also be used in active learning of the Bayesian networks, in which case the sensitivity can be used as a criterion guiding active data selection.