A method of Bayesian factor which can estimate the degree of confidence of model for reliability assessment is presented.

In order to solve the problem of model selection by means of Bayesian method and in view of the selection of the traditional linear Box-Cox model and the nonlinear Box-Cox model, the method of path sampling was adopted to calculate the Bayesian factors, A continuous path parameter with a certain assumed probability distribution was then introduced to connect different models to be selected.

Computation of Bayes factor for general nonlinear structural equation model;

Bayes factor is the major tool for model selection in Bayesian Statistics.

Calculating posterior probabilities and related Bayes factors for a collection of competing models has been a difficult and challenging problem for Bayesian statisticians.

Focused on model uncertainty among frequency analysis by the method of Bayesian model selection and Bayesian model averaging(BMA),the theory of Bayes factors approach to model selection and model averaging is introduced.

Based on Vector Autoregressive model of residents consumption,using Markov Chain Monte Carlo(MCMC) simulation combined with Bayes factors,unit root tests are conducted for rural residents consumption and urban residents consumption respectively.

From the initial stage of probabilistic Bayesian network construction to the flourishing stage of causal Bayesian network structure learning, this paper firstly reviews Bayesian network structure learning.

In consideration of differences between several feedback strategies, the progress of the research on quantum feedback control theory is reviewed, Markovian quantum feedback, Bayesian quantum feedback, non-Markovian quantum feedback with time delay and coherent quantum feedback are analyzed .