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

Uncertain evidence in Bayesian networks

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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 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.

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Notes

  1. One article briefly mentions the three types of methods of propagation of uncertain evidence in a Bayesian network [7].

  2. The software ProBT of Probayes proposes the use of a new variable named “coherence variable” to take into account new information specified by a local probability distribution [8]. Further studies remain to be carried out to compare this proposition with the propagation of likelihood evidence and probabilistic evidence.

  3. the terms of a likelihood ratio do not need to sum to one.

  4. We use the Bayesian software Netica, Menu: Enter finding / function: calibration.

  5. There seems to be an error in the results displayed in Table 2 and 3 in [19] since they do not correspond to the results announced in the text and referring to these tables.

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Authors and Affiliations

  1. LAMIH, UMR CNRS 8201 (Laboratory of Industrial and Human Automation control, Mechanical engineering and Computer Science), University of Valenciennes and Hainaut-Cambresis, Le mont Houy, F59313, Valenciennes, CEDEX 9, France

    Ali Ben Mrad, Véronique Delcroix & Sylvain Piechowiak

  2. Computer & Embedded Systems (CES Lab.), National Engineering School of Sfax (ENIS), University of Sfax, 3038, Sfax, Tunisia

    Ali Ben Mrad & Mohamed Abid

  3. Centre for Renewable Energy Systems Technology (CREST), Loughborough University Science and Enterprise Parks, LE11 3TU, Leicestershire, UK

    Philip Leicester

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  1. Ali Ben Mrad
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Correspondence to Véronique Delcroix.

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Mrad, A.B., Delcroix, V., Piechowiak, S. et al. An explication of uncertain evidence in Bayesian networks: likelihood evidence and probabilistic evidence. Appl Intell 43, 802–824 (2015). https://doi.org/10.1007/s10489-015-0678-6

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