先验信息有偏时Bayes估计的PPC优良性条件

Bayes估计在对测量数据进行处理时,充分利用了参数的先验信息和适时的观测信息.在先验信息正确的前提下,Bayes估计相对于LS估计具有Posterior Pitman Closenes即PPC优良性.然而,在许多情况下,先验信息具有主观性,不可避免地存在偏差.利用有偏的先验信息得到的Bayes估计可能不具有这种优良性,为此,给出了这种情况下Bayes估计具有PPC优良性的一个充要条件.鉴于一般情况下先验的精确分布是未知的,用实例给出了一种选取先验方差的方法,用这种方法得到的Bayes估计具有PPC优良性.

A condition of PPC superiority of Bayes estimator with inaccurate prior

Bayes estimator has been widely used in surveying data processing. Its advantage is that it can make use of not only the information contained in the observation, but also the prior information. If the prior information is accurate, the Bayes estimator has the Posterior Pitman Closenes((i.e. PPC)) superiority compared with the least square estimator. Under most conditions, the prior information is subjective. The subjective information is not accurate and there is inevitably deviation. So the Bayes estimation has not the PPC superiority if it is induced from the prior information containing deviation. In the paper, a sufficient and necessary condition of PPC superiority under prior inaccuracy is derived. Because the precise distribution of prior information is unknown, a example was given to illustrate the way to select the prior variance. In this case the Bayes estimator still has the PPC superiority.