Research On Bayesian Models With Application To Chaotic Time Series Analysis

Chaotic time series have noise arrived from practical measure,which affect parameters calculation and the next prediction precision.The dissertatior studies bayesian theory and method.And we integrate bayesian method with the other models to construct denoising models and prediting models of noisy chaotic time series. The main results in this dissertation are outlined as follows.(1)We presented a chaotic time series statistical denoising method in wavelet domain based on the idea of markov model and experiential bayes. The dual-tree complex wavelet decomposed chaotic time series with additive gaussian noise to obtain real part and imaginary part of wavelet coefficients. We modeled the real part and imaginary part data as hidden markov trees model. Empirical Bayesian method was used to estimate wavelet coefficients real part and imaginary part of source chaotic time series. Finally using dual-tree complex wavelet inverse transform, we can get the denoised chaotic time series. The numerical experiments results show that the proposed method is efficient. It can better correct the position of data points in phase space and approximate the real chaotic attractor trajectories more closely.(2) Using RBF neural networks and hierarchical bayesian algorithm,a phase space domain prediction method of noisy chaotic time series was constructed. The hierarchical bayesian algorithm treated the numbers of radial function,model parameters,and noise parameters as random variables that need to be estimated in the RBF neural networks. we used the reversible jumping Markov Chain Monte Carlo (rjMCMC) method to perform the necessary computations. The numerical experiment results show our method can predict noisy chaotic time series effectively .The model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay.(3) Based on variational bayesian and phase spa;e reconstructive theory we constructed a linearly regressive prediction model in noisy chaotic time series phase space.Time series phase space was constructed.Variational bayesian method estimated the linealy regressive coefficients. The numerical experiment results show the model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay. (4) We constructed a prediction model of the chaotic time series with additive gaussian noise based on Kriging model in the phase space. The numerical experiment results show the model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay.(5) Based on the variational bayesian method and Kriging mathematical idea we constructed a noisy chaotic time series phase space domain prediction model. The numerical experiment results show our method can predict noisy chaotic time series effectively .The model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay.