Research on Sensitivity Analysis for Dynamic Bayesian Networks

Sensitivity analysis is an important method for researching the characteristic of complex system. The present algorithms of dynamic sensitivity analysis are used to deal with some special kinds of dynamic Bayesian network and their computation complexity is very high. Therefore, in order to handle the sensitivity analysis on general dynamic Bayesian network effectively, a new algorithm is presented based on junction-tree algorithm (DSA_JT). The function relations between parameters and conditions probability distribution of object node are established by message-propagation on junction-tree. DSA_JT can lower exponential time and reduce calculation significantly. But its computation complexity is still high. In order to further improve the computational performance, DSA_BK is introduced based on DSA_JT algorithm. DSA_BK introduces the factor idea with the product of the probability of the subsystems to approximate the probability of the whole system. DSA_BK reduces the size of the root by the local marginalisation of interface and updating the joint probability distribution of model. Compared with DSA_JT, DSA_BK can lower the computational exponential times further and significantly improves the calculation efficiency, and the error is bound to be proved. Then, based on abstracting the process of the two algorithms, the computation formulas of dynamic sensitivity function are proved, and it is shown that the two algorithms can effectively deal with sensitivity analysis of general dynamic Bayesian network. Finally, the effectiveness is proved in the experiment on the network of the Shanghai Stock.