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Paraconsistent Sensitivity Analysis for Bayesian Significance Tests

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Advances in Artificial Intelligence – SBIA 2004 (SBIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3171))

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Abstract

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of using the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed.

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References

  1. Abe, J.M., Avila, B.C., Prado, J.P.A.: In: ICCIMA 1998. 2nd International Conference on Computational Intelligence and Multimidia Applications, Traralgon, Australia (1998)

    Google Scholar 

  2. Alcantara, J., Damasio, C.V., Pereira, L.M.: Paraconsistent Logic Programs. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 345–356. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Arieli, O., Avron, A.: Reasoning with Logical Bilattices. Journal of Logic, Language and Information 5, 25–63 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A First Course in Order Statistics. Wiley, New York (1992)

    MATH  Google Scholar 

  5. Barros, C.M., Costa, N.C.A., Abe, J.M.: Tópicos de Teoria dos Sistemas Ordenados. Lógica e Teoria da Ciência, 17,18,19. IEA, Univ. São Paulo (1995)

    Google Scholar 

  6. Belnap, N.D.: A useful four-valued logic. In: Epstein, G., Dumm, J. (eds.) Modern uses of Multiple Valued Logics, pp. 8–37. Reidel, Dordrecht (1977)

    Google Scholar 

  7. Boothby, W.: An Introduction to Differential Manifolds and Riemannian Geometry. Academic Press, London (2002)

    Google Scholar 

  8. Costa, N.C.A., Subrahmanian, V.S.: Paraconsistent Logics as a Formalism for Reasoning about Inconsistent Knowledge Bases. Artificial Inteligence in Medicine 1, 167–174 (1989)

    Article  Google Scholar 

  9. Costa, N.C.A., Abe, J.M., Subrahmanian, V.S.: Remarks on Annotated Logic. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 37, 561–570 (1991)

    MATH  Google Scholar 

  10. Darwiche, A.Y., Ginsberg, M.L.: A Symbolic Generalization of Probability Theory. In: AAAI-92. 10th Natnl. Conf. on Artificial Intelligence, San Jose, USA (1992)

    Google Scholar 

  11. Dugdale, J.S.: Entropy and its Physical Meaning. Taylor-Francis, London (1996)

    Book  Google Scholar 

  12. Epstein, G.: Multiple-Valued Logic Design. Inst.of Physics, Bristol (1993)

    Google Scholar 

  13. Evans, M.: Bayesian Inference Procedures Derived via the Concept of Relative Surprise. Communications in Statistics 26, 1125–1143 (1997)

    Article  MATH  Google Scholar 

  14. Fitting, M.: Logic Programming on a Topological Bilattice. Fundamentae Informaticae 11, 209–218 (1988)

    MATH  MathSciNet  Google Scholar 

  15. Fitting, M.: Bilattices and Theory of Truth. J. Phil. Logic 18, 225–256 (1989)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  17. Ginsberg, M.L.: Multivalued Logics. Computat. Intelligence 4, 265–316 (1988)

    Article  Google Scholar 

  18. Gokhale, D.V.: On Joint Conditional Enptropies. Entropy Journal 1, 21–24 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Good, I.J.: Good Thinking. Univ. of Minnesota (1983)

    Google Scholar 

  20. Good, I.J.: Surprise indices and p-values. J. Statistical Computation and Simulation 32, 90–92 (1989)

    Article  Google Scholar 

  21. Kapur, J.N.: Maximum Entropy Models in Science Engineering. Wiley, New York (1989)

    MATH  Google Scholar 

  22. Lauretto, M., Pereira, C.A.B., Stern, J.M., Zacks, S.: Comparing Parameters of Two Bivariate Normal Distributions Using the Invariant FBST. Brazilian Journal of Probability and Statistics (2004) (to appear)

    Google Scholar 

  23. Madruga, M.R., Esteves, L.G., Wechsler, S.: On the Bayesianity of Pereira-Stern Tests. Test 10, 291–299 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  24. Madruga, M.R., Pereira, C.A.B., Stern, J.M.: Bayesian Evidence Test for Precise Hypotheses. Journal of Statistical Planning and Inference 117, 185–198 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  25. Pereira, C.A.B., Stern, J.M.: Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses. Entropy Journal 1, 69–80 (1999)

    Article  Google Scholar 

  26. Pereira, C.A.B., Stern, J.M.: Model Selection: Full Bayesian Approach. Environmetrics 12, 559–568 (2001)

    Article  Google Scholar 

  27. Perny, P., Tsoukias, A.: On the Continuous Extension of a Four Valued Logic for Preference Modelling. In: IPMU-1998. 7th Conf. on Information Processing and Management of Uncertainty in Knowledge Based Systems, Paris, France (1998)

    Google Scholar 

  28. Stern, J.M., Zacks, S.: Testing the Independence of Poisson Variates under the Holgate Bivariate Distribution. The Power of a new Evidence Test. Statistical and Probability Letters 60, 313–320 (2002)

    MATH  MathSciNet  Google Scholar 

  29. Stern, J.M.: Significance Tests, Belief Calculi, and Burden of Proof in Legal and Scientific Discourse. Laptec-2003, 4th Cong. Logic Applied to Technology. Frontiers in Artificial Intelligence and its Applications 101, 139–147 (2003)

    Google Scholar 

  30. Abe, J.M., Avila, B.C., Prado, J.P.A.: In: ICCIMA 1998. 2nd International Conference on Computational Intelligence and Multimidia Applications, Traralgon, Australia (1998)

    MATH  Google Scholar 

  31. Zellner, A.: Introduction to Bayesian Inference in Econometrics. Wiley, NY (1971)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. BIOINFO and Computer Science Dept, University of São Paulo,  

    Julio Michael Stern

Authors
  1. Julio Michael Stern
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Editor information

Editors and Affiliations

  1. Instituto de Informática, UFRGS, Porto Alegre, RS, Brasil

    Ana L. C. Bazzan

  2. Intelligent Systems Laboratory LSI, Center of Technology, Federal University of Maranao UFMA, Bacanga Campus, 65080-040, Sao Luis, MA, Brazil

    Sofiane Labidi

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Stern, J.M. (2004). Paraconsistent Sensitivity Analysis for Bayesian Significance Tests. In: Bazzan, A.L.C., Labidi, S. (eds) Advances in Artificial Intelligence – SBIA 2004. SBIA 2004. Lecture Notes in Computer Science(), vol 3171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28645-5_14

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  • DOI: https://doi.org/10.1007/978-3-540-28645-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23237-7

  • Online ISBN: 978-3-540-28645-5

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