Bayesian approximation and invariance of Bayesian belief functions

The Dempster-Shafer theory is being applied for handling uncertainty in various domains. Many methods have been suggested in the literature for faster computation of belief which is otherwise exponentially complex. Bayesian approximation is one such method. In this paper, we first present some results on invariance of Bayesian belief functions under Dempster's combination rule. Based on this, we interpret Bayesian approximation and further show that it inherits these properties from the combination operator of Dempster's combination rule. Finally, we bring into focus the limitation of Bayesian approximation.