Research on fusion method for prior distribution based on the second maximum likelihood estimation theory

How to acquire proper prior distribution is a key problem in Bayesian analysis. Aiming at the over-reliance on expert's information currently in multiple information fusion, a new method based on the second maximum likelihood estimation theory to determine the weight of the prior distribution is proposed. According to the method, prior information is combined with field test data which is seen as the sample generated by the marginal distribution. The impact on the multiple information fusion of different prior distributions is determined by the magnitude of likelihood of the field sample that appears under different prior distributions and thus the weight factors of different prior distributions are determined. An example is given to show that the method proposed is more reasonable and more effective than the fusion method based on expert's information.