An explication of uncertain evidence in Bayesian networks: likelihood evidence and probabilistic evidence

Abstract

This paper proposes a systematized presentation and a terminology for observations in a Bayesian network. It focuses on the three main concepts of uncertain evidence, namely likelihood evidence and fixed and not-fixed probabilistic evidence, using a review of previous literature. A probabilistic finding on a variable is specified by a local probability distribution and replaces any former belief in that variable. It is said to be fixed or not fixed regarding whether it has to be kept unchanged or not after the arrival of observation on other variables. Fixed probabilistic evidence Véronique Delcroix Science and Enterprise Parks, LE11 3TU Leicestershire, UK is defined by Valtorta et al. (J Approx Reason 29(1):71-106 2002) under the name soft evidence, whereas the concept of not-fixed probabilistic evidence has been discussed by Chan and Darwiche (Artif Intell 163(1):67-90 2005). Both concepts have to be clearly distinguished from likelihood evidence defined by Pearl (1988), also called virtual evidence, for which evidence is specified as a likelihood ratio, that often represents the unreliability of the evidence. Since these three concepts of uncertain evidence are not widely understood, and the terms used to describe these concepts are not well established, most Bayesian networks engines do not offer well defined propagation functions to handle them. Firstly, we present a review of uncertain evidence and the proposed terminology, definitions and concepts related to the use of uncertain evidence in Bayesian networks. Then we describe updating algorithms for the propagation of uncertain evidence. Finally, we propose several results where the use of fixed or not-fixed probabilistic evidence is required.

Dynamic Bayesian Network Inferencing for Non-Homogeneous Complex Systems

“…This contrasts with fixed probabilistic evidence (which is also referred to as soft evidence) approaches, typically based on an iterative proportional fitting procedure, where the marginal remains unchanged despite the introduction of further evidence (Mrad et al ., ). However, soft‐evidence‐based inferencing is not necessarily consistent with maximum a posteriori inferencing.…”

“…The evidence E corresponds to observations of the system. There are three main types of evidence (Mrad et al, 2015). Hard evidence corresponds to an observation of some state x such that P.X = x/ = 1 and is supported by all inference algorithms.…”

Probabilistic evaluation of solar photovoltaic systems using Bayesian networks: a discounted cash flow assessment

“…Secondly, the evidence establishes a new probability distribution on the observed variable. This is referred to as uncertain evidence of which there are two types-likelihood evidence where the observation is uncertain and probabilistic evidence where the evidence specifies the new local distribution [14].…”

“…A number of commercial and open-source software applications exist for creating BN models [14]. These provide a graphical user interface for constructing the graphical model, a method to import or learn marginal and conditional probability distributions and features to apply either hard or uncertain evidence to one or more nodes.…”

“…Assuming no additional non-warranted expenditures for repair and maintenance, and neglecting decommissioning costs, the total NPV is given by Eqn (14).…”