Applied Intelligence

, Volume 43, Issue 4, pp 802–824 | Cite as

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

Uncertain evidence in Bayesian networks
  • Ali Ben Mrad
  • Véronique DelcroixEmail author
  • Sylvain Piechowiak
  • Philip Leicester
  • Mohamed Abid


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 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.


Bayesian network Uncertain evidence Probabilistic evidence Likelihood finding Soft evidence Virtual evidence 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.LAMIH, UMR CNRS 8201 (Laboratory of Industrial and Human Automation control, Mechanical engineering and Computer Science)University of Valenciennes and Hainaut-CambresisValenciennesFrance
  2. 2.Computer & Embedded Systems (CES Lab.), National Engineering School of Sfax (ENIS)University of SfaxSfaxTunisia
  3. 3.Centre for Renewable Energy Systems Technology (CREST)Loughborough University Science and Enterprise ParksLeicestershireUK

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