Belief Update in Bayesian Networks Using Uncertain Evidence

This paper reports our investigation on the problem of belief update in Bayesian networks (BN) using uncertain evidence. We focus on two types of uncertain evidences, virtual evidence (represented as likelihood ratios) and soft evidence (represented as probability distributions). We review three existing belief update methods with uncertain evidences: virtual evidence method, Jeffrey´s rule, and IPFP (iterative proportional fitting procedure), and analyze the relations between these methods. This in-depth understanding leads us to propose two algorithms for belief update with multiple soft evidences. Both of these algorithms can be seen as integrating the techniques of virtual evidence method, IPFP and traditional BN evidential inference, and they have clear computational and practical advantages over the methods proposed by others in the past