关键词: 先验信息融合, 贝叶斯, 最大熵原理, 充分性, 灰色关联分析

Abstract:

The exploration of Bayesian prior information has long been an important and hot topic in the field， especially in the Bayes evaluation process of small-sample experiments， where prior information has a significant impact on the accuracy of the evaluation results. Traditional methods have significant flaws in mining prior information from historical samples of multiple heterogeneous small samples. The fusion using related statistical methods only mines correlations from the prior sample data itself， lacking consideration of comprehensiveness. Methods that consider the fusion of expert knowledge demand too high a level of cognition （knowledge and experience） from experts， requiring evaluation of issues that are difficult to judge and assess. Due to these issues， the effectiveness of prior sample utilization is often unsatisfactory， and may even lead to significant errors.Therefore， a new Bayesian prior information hybrid regenerative grey entropy weight model is proposed. Firstly， sample grey incidence mining is conducted， and adequacy indicators are designed based on the number of sample sub-samples. Secondly， with hybrid of their incidence and adequacy， an importance indicator for the prior sample is established. Then， based on sample importance， a maximum entropy model for weight configuration of regenerated weights of multiple prior samples is constructed. Finally， by weighted fusion regeneration into new prior samples， a more accurate posterior distribution is obtained， effectively addressing the problem of hybrid regeneration of Bayesian prior information.The effectiveness and scientific validity of the model are validated through multiple aerospace practical application cases such as the China Academy of Launch Vehicle Technology， China Academy of Space Technology， and Shanghai Academy of Aerospace Technology. The model in this paper is mainly applied in the reliability design of large and complex equipment in the aviation and aerospace fields including rockets and satellites. Its reliability testing is costly， and the obtainable sample data is small. At the same time， the data exhibits typical characteristics of multiple heterogeneous sources， with low information value density， leading to objective limitations in cognition and randomness. The method proposed in this paper is more conducive to improving the information fusion quality of Bayesian methods in reliability assessment problems， thereby making more correct decisions.

Key words: prior information fusion, Bayesian theory, maximum entropy, adequacy, grey incidence analysis