Cognitive constructivism and Bayesian statistics

Authors

  • Julio Michael Stern Universidade de São Paulo. Instituto de Matemática e Estatística

DOI:

https://doi.org/10.1590/S1678-31662006000400003

Keywords:

Autopoiesis, Eigen-solutions, Cognitive constructivism, Epistemology, Sharp hypotheses, Statistical significance, Systems theory

Abstract

In this paper, some epistemological, ontological, and sociological issues are investigated, concerning the statistical significance of sharp hypotheses in scientific research, within the framework offered by cognitive constructivism and FBST - the full Bayesian significance test. The constructivist framework is contrasted to those furnished by decision theory and falsificationism, the traditional epistemological approaches to orthodox Bayesian statistics and to frequentist statistics.

Downloads

Download data is not yet available.

References

Bakken, T. & Hernes, T. Autopoietic organization theory: drawing on Niklas Luhmann’s social systems perspective. Copenhagen: Copenhagen Business School, 2002.

Bertalanffy, L. von. General system theory. New York: George Braziller, 1969.

Birnbaum, Z. W.; Esary, J. D. & Saunders, S. C. Multicomponent systems and structures, and their reliability. Technometrics, 3, p. 55-77, 1961.

Borges, W. & Stern, J. M. On the truth value of complex hypotheses. CIMCA-2005: International conference on computational intelligence for modelling control and automation. Los Alamitos: IEEE, 2005.

Boyd, R.; Gasper, P. & Trout, J. D. The philosophy of science. Cambridge: MIT Press, 1991.

Caygill, H. A Kant dictionary. Oxford: Blackwell, 1995.

Christis, J. Luhmann’s theory of knowledge: beyond realism and constructivism? Soziale Systeme, 7, p. 328-49, 2001.

Darwiche, A. Y. A symbolic generalization of probability theory. Stanford: Stanford University Press, 1993.

Darwiche, A. Y. & Ginsberg, M. L. A symbolic generalization of probability theory. Proceedings of the 10th national conference on artificial intelligence, 1992. p. 622-7. (AAAI-92. )

Diaconis, P. Group representation in probability and statistics, 1988. (Institute of Mathematical Statistics Lecture Notes 11. )

Diaconis, P. & Freeman, D. A dozen de Finetti style results in search of a theory. Annales de l’Institute Henri Poincaré, Probabilité et Statistique, 23, p. 397-423, 1987.

DiMaggio, P. & Powell, W. W. New institutionalism in organizational analysis. Chicago: Chicago University Press, 1991.

Doncel, M. G.; Hermann, A.; Michel, L. & Pais, A. Symmetries in physics (1600-1980). Barcelona: Seminari d’Història des les Ciènces, Universitat Autònoma de Barcelona, 1987.

Dubins, L. E. & Savage, L. J. How to gamble if you must: inequalities for stochastic processes. New York: McGraw-Hill, 1965.

Dugdale, J. S. Entropy and its physical meaning. London: Taylor & Francis, 1996.

Eaton, M. L. Group invariance applications in statistics. Hayward: Institute of Mathematical Statistics and American Statistical Association, 1989.

Feller, W. An introduction to probability theory and its applications. New York: Wiley, 1971.

Finetti, B. de. Theory of probability. London: Wiley, 1974. 2 v.

Finetti, B. de. Scritti. Padova: Cedam, 1981. v. 1.

Finetti, B. de. Scritti. Padova: Cedam, 1991. v. 2.

Finetti, B. de. Probabilitá e induzione. Bologna: Clueb, 1993.

Foerster, H. von. Understanding understanding: essays on cybernetics and cognition. New York: Springer, 2003.

French, A. P. Special relativity. New York: Chapman & Hall, 1968.

Fuchs, S. The new wars of truth: conflicts over science studies as differential modes of observation. Social Science Information, 35, p. 307-26, 1996.

Good, I. J. Good thinking. Minneapolis: University of Minnesota Press, 1983.

Gruber, B. et al. (Ed. ). Symmetries in science. New York: Plenum, 1980-98. 9 v.

Harlow, L. L.; Mulaik, S. A. & Steiger, J. H. What if there were no significance tests? London: Lawrence Erlbaum, 1997.

Hayakawa, Y.; Irony, T. Z. & Xie, M. (Org. ). Systems and Bayesian reliability. Singapore: World Scientific, 2002.

Irony, T. Z. & Pereira, C. A. B. Bayesian hypothesis test: using surface integrals to distribute prior information among the hypotheses. Resenhas do Instituto de Matemática e Estatística da Universidade de São Paulo, 2, 27-46, 1995.

Irony, T. Z.; Pereira, C. A. B. & Tiwari, R. C. Analysis of opinion swing: comparison of two correlated proportions. The American Statistician, 54, 57-62, 2000.

Irony, T. Z.; Lauretto, M.; Pereira, C. A. B. & Stern, J. M. A Weibull wearout test: full Bayesian approach. In: Hayakawa, Y.; Irony, T. Z. & Xie, M. (Org. ). Systems and Bayesian reliability. Singapore: World Scientific, 2002. p. 287-300.

Jaffe, B. Michelson and the speed of light. New York: Anchor, 1960.

Kant, I. Crítica da faculdade do juízo. Tradução V. Rohden & A. Marques. Rio de Janeiro: Forense Universitária, 1995 [1790].

Kapur, J. N. Maximum entropy models in science and engineering. New York: Wiley, 1989.

Krohn, W. & Küppers, G. The selforganization of science: outline of a theoretical model. In: Krohn, W.; Küppers, G. & Nowotny, H. (Org. ). Selforganization: portrait of a scientific revolution. Dordrecht: Kluwer, 1990. p. 208-22.

Landau, L. D. & Lifschitz, E. M. Cours de physique théorique. Moscou: MIR, 1966.

Lauretto, M.; Pereira, C. A. B.; Stern, J. M. & Zacks, S. Comparing parameters of two bivariate normal distributions using the invariant full Bayesian significance test. Brazilian Journal of Probability and Statistics, 17, p. 147-68, 2003.

Levi, I. Gambling with truth: an essay on induction and the aims of science. Cambridge: The MIT Press, 1974.

Lorentz, H. A.; Einstein, A.; Minkowsky, H. & Weyl, H. The principle of relativity: a collection of original memoirs on the special and general theory of relativity. New York: Dover, 1952.

Luhmann, N. Ecological communication. Chicago: Chicago University Press, 1989.

Luhmann, N. The cognitive program of constructivism and a reality that remains unknown. In: Krohn, W.;

Küppers, G. & Nowotny, H. (Org. ). Selforganization: portrait of a scientific revolution. Dordrecht: Kluwer, 1990a. p. 64-86.

Küppers, G. & Nowotny, H. Essays on self-reference. New York: Columbia University Press, 1990b.

Küppers, G. & Nowotny, H. Social systems. Stanford: Stanford University Press, 1995.

Madruga, M. R.; Esteves, L. G. & Wechsler, S. On the bayesianity of Pereira-Stern tests. Test, 10, p. 291-9, 2001.

Madruga, M. R.; Pereira, C. A. B. & Stern, J. Bayesian evidence test for precise hypotheses. Journal of Statistical Planning and Inference, 117, p. 185-98, 2003.

Maher, P.; Skyrms, B.; Adams, E. W.; Binmore, K.; Butterfield, J.; Diaconis, P. & Harper, W. L. Betting on theories. Cambridge: Cambridge University Press, 1993.

Maturana, H. R. & Varela, F. J. Autopoiesis and cognition: the realization of the living. Dordrecht: Reidel, 1980.

Michelson, A. A. & Morley, E. W. On the relative motion of the earth and the luminiferous ether. American Journal of Physics, 34, p. 333-45, 1887.

Mingers, J. Self-producing systems: implications and applications of autopoiesis. New York: Plenum, 1995.

Nachbin, L. The Haar integral. Princeton: Van Nostrand, 1965.

Noether, E. Invariant varlation problems. Tradução M. A. Tavel. Transport Theory and Statistical Physics, 1, p. 183-207, 1971 [1918].

Pereira, C. A. B. & Stern, J. M. Evidence and credibility: full Bayesian significance test for precise hypotheses. Entropy Journal, 1, p. 69–80, 1999.

Pereira, C. A. B. & Stern, J. M. Model selection: full Bayesian approach. Environmetrics, 12, p. 559-68, 2001.

Petitjean, M. (Org.). Foundations of Information Science. Basel: MDPI, 2005. v. 61.

Popper, K. R. A lógica da pesquisa científica. Tradução L. Hegenberg & O. S. da Mota. São Paulo: Cultrix, 1972 [1934].

Popper, K. R. Conjecturas e refutações. Tradução S. Bath. Brasília: Editora UnB, 1974 [1963].

Rasch, W. Luhmann’s Widerlegung des Idealismus: constructivism as a two-front war. Soziale Systeme, 4, p. 151-61, 1998.

Ressel, P. A Very general de Finetti type theorem. In: Viertl, R. Probability and Bayesian statistics. New York: Plenum, 1987. p. 403-14.

Rouanet, H.; Bernard, J. M.; Bert, M. C.; Lecoutre, B.; Lecoutre, M. P. & Le Roux, B. New ways in statistical methodology: from significance tests to Bayesian inference. Berna: Peter Lang, 1998.

Savage, L. J. The foundations of statistics. New York: Dover, 1954.

Segal, L. The dream of reality: Heinz von Foerster’s constructivism. New York: Springer, 2001.

Shafer, G. Lindley’s paradox. Journal of the American Statistical Association, 77, p. 325-51, 1982.

Stern, J. M. Significance tests, belief calculi, and burden of proof in legal and scientific discourse. Frontiers in Artificial Intelligence and its Applications, 101, p. 139-47, 2003. (Laptec’03. )

Stern, J. M. Cognitive constructivism, eigen-solutions, and sharp statistical hypotheses. In: Petitjean, M. (Org.). Foundations of information science. Basel: MDPI, 2005. v. 61. p. 1-23.

Stern, J. M. & Zacks, S. Testing independence of Poisson variates under the Holgate bivariate distribution: the power of a new evidence test. Statistical and Probability Letters, 60, p. 313-20, 2002.

Viertl, R. Probability and Bayesian statistics. New York: Plenum, 1987.

Williams, D. Weighing the odds. Cambridge: Cambridge University Press, 2001.

Wittgenstein, L. Tractatus logico-philosophicus. Tradução L. H. L. dos Santos. São Paulo: Edusp, 1993 [1921].

Zelleny, M. Autopoiesis, dissipative structures, and spontaneous social orders. Washington: American Association for the Advancement of Science, 1980.

Published

2006-12-01

Issue

Section

Artigos

How to Cite

Cognitive constructivism and Bayesian statistics . (2006). Scientiae Studia, 4(4), 598-613. https://doi.org/10.1590/S1678-31662006000400003