Abstract
In this paper, we discuss the problem of combining several pieces of uncertain evidence, such as provided by symptoms, expert opinions, or sensor readings. Several of the proposed methods for combining evidence are reviewed and criticized. We argue for the position that (1) in general these proposed methods are inadequate, (2) strictly speaking, the only justifiable solution is to carefully model the situation, (3) a careful modelling of the situation requires a distinction between ignorance and uncertainty, and (4) drawing useful conclusions in the presence of ignorance may require additional assumptions which are not derivable from the available evidence.
The investigations were carried out as part of the PIONIER-project Reasoning with Uncertainty, subsidized by the Netherlands Organization of Scientific Research (NWO), under grant pgs-22–262.
Preview
Unable to display preview. Download preview PDF.
References
J.O. Berger, Statistical Decision Theory and Bayesian Analysis (Springer, Berlin, 1985).
A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics 38 (1967) 325–339.
C. Genest and J. Zidek, Combining probability distributions: a critique and an annotated bibliography, Statistical Science 1 (1986) 114–148.
J.Y. Halpern and R. Fagin, Two views of belief: belief as generalized probability and belief as evidence, Artificial Intelligence 54 (1992) 275–317.
R. Johnson, Independence and Bayesian updating methods, Artificial Intelligence 29 (1986) 217–222.
H.E. Kyburg, Bayesian and non-Bayesian evidential updating, Artificial Intelligence 31 (1987) 271–293. (Addendum: Artificial Intelligence 36 (1988) 265–266.)
R.E. Neapolitan, A note of caution on combining certainties, International Journal of Pattern Recognition and Artificial Intelligence 1 (1987) 427–433.
D. Pagac, E.M. Nebot, and H. Durrant-Whyte, An evidential approach to probabilistic map-building, in: L. Dorst, M. van Lambalgen, and F. Voorbraak eds., Reasoning with Uncertainty in Robotics (Springer, Berlin, 1996) 164–170.
G. Shafer, A Mathematical Theory of Evidence (Princeton U.P., Princeton, 1976).
P. Smets, Belief functions versus probability functions, in: B. Bouchon, L. Aitt, R.R. Yager, eds., Uncertainty and Intelligent Systems, LNCS 313 (Springer, Berlin, 1988) 17–24.
P. Smets and R. Kennes, The transferable belief model, Artificial Intelligence 66 (1994) 191–234.
F. Voorbraak, On the justification of Dempster's rule of combination, Artificial Intelligence 48 (1991) 499–515.
F. Voorbraak, Combining unreliable pieces of evidence, research report CT-95-07 (ILLC, University of Amsterdam, 1995).
F. Voorbraak, Probabilistic belief expansion and conditioning, research report LP-96-07 (ILLC, University of Amsterdam, 1996).
F. Voorbraak, Reasoning with uncertainty in AI, in: L. Dorst, M. van Lambalgen, and F. Voorbraak eds., Reasoning with Uncertainty in Robotics (Springer, Berlin, 1996) 164–170.
F. Voorbraak, Decision analysis using partial probability theory, Proceedings AAAI 1997 Spring Symposium Qualitative Preferences in Deliberation and Practical Reasoning LP-96-07 (Stanford University, 1997).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Voorbraak, F. (1997). Combining evidence under partial ignorance. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds) Qualitative and Quantitative Practical Reasoning. FAPR ECSQARU 1997 1997. Lecture Notes in Computer Science, vol 1244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035650
Download citation
DOI: https://doi.org/10.1007/BFb0035650
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63095-1
Online ISBN: 978-3-540-69129-7
eBook Packages: Springer Book Archive