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Comparison of Quantum and Bayesian Inference Models

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Quantum Interaction (QI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5494))

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Abstract

The mathematical principles of quantum theory provide a general foundation for assigning probabilities to events. This paper examines the application of these principles to the probabilistic inference problem in which hypotheses are evaluated on the basis of a sequence of evidence (observations). The probabilistic inference problem is usually addressed using Bayesian updating rules. Here we derive a quantum inference rule and compare it to the Bayesian rule. The primary difference between these two inference principles arises when evidence is provided by incompatible measures. Incompatibility refers to the case where one measure interferes or disturbs another measure, and so the order of measurement affects the probability of the observations. It is argued that incompatibility often occurs when evidence is obtained from human judgments.

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References

  1. Aerts, D., Broekaert, J., Gabora, L.: A Case for Applying an Abstracted Quantum Formalism to Cognition. In: Campbell, R. (ed.) Mind in Interaction. John Benjamin, Amsterdam (2003)

    Google Scholar 

  2. Bordley, R.F.: Quantum Mechanical and Human Violations of Compound Probability Principles: Toward a Generalized Heisenberg Uncertainty Principle. Operations Research 46, 923–926 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Busemeyer, J.R., Wang, Z., Townsend, J.T.: Quantum Dynamics of Human Decision Making. Journal of Mathematical Psychology 50(3), 220–241 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Degroot, M.H.: Optimal Statistical Decisions. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  5. Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press, Oxford (1930, 2001)

    MATH  Google Scholar 

  6. Franco, R.: The Conjunction Fallacy and Interference Effects. Journal of Mathematical Psychology (2007) (to appear), arXiv:0708.3948v1 [physics.gen-ph]

    Google Scholar 

  7. Guder, S.P.: Stochastic Methods in Quantum Mechanics. Dover Press (1979)

    Google Scholar 

  8. Hayashi, M.: Quantum Information Theory: An Introduction. Springer, Berlin (2006)

    MATH  Google Scholar 

  9. Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)

    MATH  Google Scholar 

  10. Holevo, A.S.: Statistical Structure of Quantum Mechanics. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  11. Khrennikov, A.: Can Quantum Information be Processed by Macroscopic Systems? Quantum Information Theory (in press, 2007)

    Google Scholar 

  12. Kolmogorov, A.N.: Foundations of the Theory of Probability. Chelsea Publishing Co., New York (1950)

    MATH  Google Scholar 

  13. Laskey, K.B.: Quantum Causal Networks. In: Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.) Proceedings of the AAAI Spring Symposium on Quantum Interaction, Stanford University, March 27-29. AAAI Press, Menlo Park (2007)

    Google Scholar 

  14. Luders, G.: Uber die Zustandsanderung durch den Messprozess. Annalen der Physik 8, 322–328 (1951)

    MathSciNet  MATH  Google Scholar 

  15. La Mura, P., Swiatczak, L.: Markov Entanglement Networks. In: Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.) Proceedings of the AAAI Spring Symposium on Quantum Interaction, Stanford University, March 27-29. AAAI Press, Menlo Park (2007)

    Google Scholar 

  16. Pitowski, I.: Quantum Probability, Quantum logic. Lecture Notes in Physics, vol. 321. Springer, Heidelberg (1989)

    Google Scholar 

  17. Tucci, R.R.: Quantum Bayesian Nets (1997) quantph/9706039

    Google Scholar 

  18. Von Neumann, J.: Mathematical Foundations of Quantum Theory. Princeton University Press, Princeton (1932)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Cognitive Science, Indiana University, 1101 E. 10th Street, Bloomington, Indiana, 47405, USA

    Jerome R. Busemeyer & Jennifer Trueblood

Authors
  1. Jerome R. Busemeyer
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  2. Jennifer Trueblood
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Editor information

Editors and Affiliations

  1. Faculty of Science and Technology, Queensland University of Technology, GPO Box 2434, 4001, Brisbane, Australia

    Peter Bruza

  2. Naval Research Laboratory, Navy Center for Applied Research in Artificial Intelligence, 4555 Overlook Avenue S.W, DC 20375, Washington, USA

    Donald Sofge

  3. Paine College, 1235 15th Street, P.O. Box, GA 30901-3182, Augusta, USA

    William Lawless

  4. Department of Computing Science, University of Glasgow, 17 Lilybank Gardens, G12 8QQ, Glasgow, UK

    Keith van Rijsbergen

  5. German Research Center for Artificial Intelligence, Stuhlsatzenhausweg 3, 66123, Saarbrücken, Germany

    Matthias Klusch

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© 2009 Springer-Verlag Berlin Heidelberg

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Busemeyer, J.R., Trueblood, J. (2009). Comparison of Quantum and Bayesian Inference Models. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds) Quantum Interaction. QI 2009. Lecture Notes in Computer Science(), vol 5494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00834-4_5

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  • DOI: https://doi.org/10.1007/978-3-642-00834-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00833-7

  • Online ISBN: 978-3-642-00834-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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