Understanding soft evidence as probabilistic evidence: Illustration with several use cases

This paper aims to get a better understanding of the notions of evidence, probabilistic evidence and likelihood evidence in Bayesian Networks. Evidence comes from an observation of one or several variables. Soft evidence is probabilistic evidence, since the observation consists in a local probability distribution on a subset of variables that has to replace any former belief on these variables. It has to be clearly distinguished from likelihood evidence, also called virtual evidence, for which the evidence is specified as a likelihood ratio. Since the notion of soft evidence is not yet widely understood, most of the Bayesian Networks engines do not propose related propagation functions and the terms used to describe such evidence are not stabilised. First, we present the different types of evidence on a simple example with an illustrative context. Then, we discuss the understanding of both notions in terms of knowledge and observation. Next, we propose to use soft evidence to represent certain evidence on a continuous variable, after fuzzy discretization.