Research And Application On Sensitivity Analysis For Dynamic Bayesian Networks

Sensitivity analysis is the study for the propagation of the changes in the value ofthe parameter.It is used for quantify analysis the importance of system parametersand structure. it is applied widely in the system analysis and discover of anomalycharacteristics. But the present algorithms of dynamic sensitivity analysis is hautnedby high computational complexity, or can only be applied to the part of the problems.This paper provides two algorithms DSA_JT and DSA_BK, to solve this problem.The main contents of this dissertation are as follows:Firstly, this dissertation makes a briefly introduction of the BNs, The sensitivityanalysis, and some related research state and development trend of exchange rateprecdiction.Secondly,the present algorithms of dynamic sensitivity analysis are for somespecial kinds of simple Dynamic Bayesian network and computation complexity isvery high. Therefore, In order to handle sensitivity analysis on general DynamicBayesian network effectively, a new algorithm is presented which based onjunction-tree algorithm (DSA_JT). The function relations between parameters andconditions probability distribution of object node is established bymessage-propagation on junction-tree. DSA_JT can lower exponential time andsignificantly reduce calculation. But its computation complexity is still high. In orderto further improve the computational performance, DSA_BK is introduced based onDSA_JT algorithm. DSA_BK introduces the factor idea with the product of theprobability 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 andupdating the joint probability distribution of model. Compared with DSA_JT,DSA_BK can lower the computational exponential times further and significantlyimproves the calculation efficiency, and the error is bound to be proved. Then, basedon abstracting the process of the two algorithms, the computation formulas ofdynamic sensitivity function are proved, and it shows that the two algorithms caneffectively deal with sensitivity analysis of general Dynamic Bayesian Network.Lastly, the effectiveness of DSA_JT and DSA_BK is showed in the experiment onthe network of the Shanghai stock,and show it better for predictioning rate when it works with ARMA model than normal ARMA model.