Pair-Copula Bayesian Networks Model Based On Polynomial Regression

With the rapid development of Internet technology,the data volume from all fields is rapidly expanding,people are increasingly aware of the importance of data.How to effectively convert data into useful knowledge,is the challenge we face.Dependency relationship is a common form of relationship between variables,but it is often uncertain and indirect.Analysis of the dependency relationship between variables plays an important role for our perception of the territory of a certain law.Pair-Copula Bayesian networks is a multivariate statistical model which inherits the merits of the general Bayesian networks structure and combines the excellent properties of Copula at the same time.This model can reflect the dependency relationship between variables through structure inference and correlation analysis.Compared with Vine model,PCBNs need less number of Pair-Copulas.This makes the model more intuitive and concise.Building the Pair-Copula Bayesian networks model mainly includes two parts,the structure estimation and parameter estimation.In the first part,the core step is to conduct conditional independence test between random variables.On the other hand,when the method is applied to the real engineering or management problem,its usefulness is also an important factor.Theoretical rigour and the convenience of application of the test methods need to be considered at the same time.By applying the PC-stable algorithms,we put forward the conditional independence test method based on the residuals of polynomial regression,then carry out the simulation.In the end,we carry on the empirical analysis of the hourly meteorological data in 2010 in Tianjin.The method can effectively test the conditional independence relationship between variables.Both dependent and independent relationships can be reflected by the network structure.Combining with Pair-Copula,we can obtain the complete dependency relationship model and the corresponding joint density function.