Statistical Analysis Of Global Symmetry Based On Isomorphic Symmetrical Frame

The paper is divided into four parts.The first part gives some background knowledge needed in this paper,such as the three basic principles of data analysis,the necessity of the experimental design,the defi-nition of frame and frame set. Finally,the papers gives the definition of isomorphism of frame.Isomorphic frame can be considered equivalent,in particular the symmetrical frame.The second part of the paper describes the definition of the orbital characteristics for the symmetrical frame,as well as the properties of the orbital characteristics. Then, the paper discusses how to determine the isomorphism of the symmetrical frame based on the orbital characteristics. The classification of the symmetrical frame is based on symmetrical frame isomorphism. The isomorphism frame can be considered to be equivalent,so the classification of the symmetrical frame greatly simplifies.The third part gives the definition of stable subframe based on any element σ∈G and any subgroup G'(?)G. Then the paper gives a number of its properties. Finally, according to the properties of the stable subframe, we get a powerful tool of constructing symmetrical frame.The fourth parts describes the symmetrical global sensitivity analysis. The symmet-rical global sensitivity analysis is based on symmetrical ANOVA high-dimensional model representation. Then the paper gives how to use the symmetrical frame to get the obser-vations of the experiment to do symmetrical sensitivity analysis. An example is given to show the feasibility of simulation by the symmetrical frame and the equivalence between the isomorphism symmetrical frame.