The credible sets for system parameters and transfer functions are discussedin this paper. The derivations of the credible sets via the Bayesian statistical methods aregiven in various cases and the credible sets of t...The credible sets for system parameters and transfer functions are discussedin this paper. The derivations of the credible sets via the Bayesian statistical methods aregiven in various cases and the credible sets of transfer functions are constructed on thebasis of the parameter credible sets. In the small sample case the credible set, which theparameters are in, has minimal volume with given credible probability. In the large samplecaset it is proved that if the critical boundary is taken properly then the probability, withwhich the parameters are in the credible set, will tend to one as the number of data tendsto infinity. The credible set for transfer function is an envelope on the complex plane.Under some assumptions, the envelope tends to the curve of true transfer function.展开更多
基金supported National Natural Science Foundation of China(51675272)Jiangsu Science and technology plan project(BE2019002-2)+1 种基金Science and technology plan project of Lianyungang high tech zone(ZD201909)Jiangsu blue and green engineering project and Jiangsu Graduate Research and Innovation Project Fund(KYCX202913)。
文摘The credible sets for system parameters and transfer functions are discussedin this paper. The derivations of the credible sets via the Bayesian statistical methods aregiven in various cases and the credible sets of transfer functions are constructed on thebasis of the parameter credible sets. In the small sample case the credible set, which theparameters are in, has minimal volume with given credible probability. In the large samplecaset it is proved that if the critical boundary is taken properly then the probability, withwhich the parameters are in the credible set, will tend to one as the number of data tendsto infinity. The credible set for transfer function is an envelope on the complex plane.Under some assumptions, the envelope tends to the curve of true transfer function.
