Bayesian Information Fusion for Imprecise Probabilistic Models with Different Types of Information

Abstract

A novel approximate Bayesian information fusion method is proposed based on Wasserstein distance and it is applied it to imprecise probabilistic models with different types of information. The proposed method combines the principle of maximum relative entropy with approximate Bayesian computation and uses the Wasserstein distance to perform the approximate Bayesian computations. The key benefit of this approach is the capability to handle different types of information, such as point observed data and moment information. To verify the effectiveness of the proposed method, we apply it to a simple supported beam problem. The results are analyzed towards accuracy and the proposed method is compared to the classical Bayesian approach combined with maximum relative entropy.