Admissibility of Bayes estimate with inaccurate prior in surveying adjustment①
(1. Department of Surveying Engineering, Central South University of Technology, Changsha, 410083, P.R.China;
2. The Land Management Bureau ofHuizhou, Huizhou 516000, P.R.China)
2. The Land Management Bureau ofHuizhou, Huizhou 516000, P.R.China)
Abstract: Based on the concept of admissibility in statistics, a definition of generalized admissibility of Bayes estimates has been given at first, which was with inaccurate prior for the application in surveying adjustment. Then according to the definition, the generalized admissibility of the normal linear Bayes estimate with the inaccurate prior information that contains deviations or model errors, as well as how to eliminate the effect of the model error on the Bayes estimate in surveying adjustment were studied. The results show that if the prior information is not accurate, that is, it contains model error, the generalized admissibility can explain whether the Bayes estimate can be accepted or not. For the case of linear normal Bayes estimate, the Bayes estimate can be made generally admissible by giving a less prior weight if the prior information is inaccurate. Finally an example was given.
Key words: Bayes estimate; admissibility; inaccurate prior; surveying adjustment