Gauss-Markov model is frequently used in data analysis; the analysis and estimation of its parameters is always a hot issue. Based on the information theory and from the viewpoint of optimal information on description...Gauss-Markov model is frequently used in data analysis; the analysis and estimation of its parameters is always a hot issue. Based on the information theory and from the viewpoint of optimal information on description—minimum description length, this paper discusses a case: where there is multi-collinearity in the coefficient matrix, principal component estimation is used to estimate and select the original parameters, so as to reduce its multi-collinearity and improve its credibility. From the viewpoint of minimum description length, this paper discusses the approach of selecting principal components and uses this approach to solve a practical problem.展开更多
Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational simplifications are sometimes possible, but are not generally applicable. There is a large lit...Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational simplifications are sometimes possible, but are not generally applicable. There is a large literature available on a methodology based on information theory called Minimum Description Length (MDL). It is described here how many of these techniques are either directly Bayesian in nature, or are very good objective approximations to Bayesian solutions. First, connections between the Bayesian approach and MDL are theoretically explored;thereafter a few illustrations are provided to describe how MDL can give useful computational simplifications.展开更多
基金Project(40074001) supported by National Natural Science Foundation of China Project (SD2003 -10) supported by the Open ResearchFund Programof the Key Laboratory of Geomatics and Digital Technilogy ,Shandong Province
文摘Gauss-Markov model is frequently used in data analysis; the analysis and estimation of its parameters is always a hot issue. Based on the information theory and from the viewpoint of optimal information on description—minimum description length, this paper discusses a case: where there is multi-collinearity in the coefficient matrix, principal component estimation is used to estimate and select the original parameters, so as to reduce its multi-collinearity and improve its credibility. From the viewpoint of minimum description length, this paper discusses the approach of selecting principal components and uses this approach to solve a practical problem.
文摘Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational simplifications are sometimes possible, but are not generally applicable. There is a large literature available on a methodology based on information theory called Minimum Description Length (MDL). It is described here how many of these techniques are either directly Bayesian in nature, or are very good objective approximations to Bayesian solutions. First, connections between the Bayesian approach and MDL are theoretically explored;thereafter a few illustrations are provided to describe how MDL can give useful computational simplifications.
