Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T05:09:01.967Z Has data issue: false hasContentIssue false
  • English
  • Français

Bayes, Bounds, and Rational Analysis

Published online by Cambridge University Press:  01 January 2022

Thomas F. Icard
Get access Rights & Permissions [Opens in a new window]

Abstract

While Bayesian models have been applied to an impressive range of cognitive phenomena, methodological challenges have been leveled concerning their role in the program of rational analysis. The focus of the current article is on computational impediments to probabilistic inference and related puzzles about empirical confirmation of these models. The proposal is to rethink the role of Bayesian methods in rational analysis, to adopt an independently motivated notion of rationality appropriate for computationally bounded agents, and to explore broad conditions under which (approximately) Bayesian agents would be rational. The proposal is illustrated with a characterization of costs inspired by thermodynamics.

Type
Research Article
Information
Philosophy of Science , Volume 85 , Issue 1 , January 2018 , pp. 79 - 101
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†.

This article grew out of a presentation to the Bay Bayesians meeting at the University of California, Berkeley, in February 2012, and I would like to thank everyone present there for a very helpful and formative discussion. Thanks also to David Danks, Pedro Ortega, Rob Long, and Richard Samuels for helpful conversations and comments on the article.

References

Anderson, J. R. 1990. The Adaptive Character of Thought. Mahwah, NJ: Erlbaum.Google Scholar
Bowers, J. S., and Davis, C. J.. 2012. “Bayesian Just-So Stories in Psychology and Neuroscience.” Psychological Bulletin 138 (3): 389–414..CrossRefGoogle ScholarPubMed
Chater, N., and Oaksford, M.. 1999. “Ten Years of the Rational Analysis of Cognition.” Trends in Cognitive Science 3 (2): 57–65..CrossRefGoogle ScholarPubMed
Danks, D. 2008. “Rational Analyses, Instrumentalism, and Implementations.” In The Probabilistic Mind: Prospects for Bayesian Cognitive Science, ed. Chater, N. and Oaksford, M., 59–75. Oxford: Oxford University Press.CrossRefGoogle Scholar
Daw, N. D., Courville, A. C., and Dayan, P.. 2008. “Semi-rational Models of Conditioning: The Case of Trial Order.” In The Probabilistic Mind: Prospects for Bayesian Cognitive Science, ed. Chater, N. and Oaksford, M., 431–52. Oxford: Oxford University Press.Google Scholar
de Finetti, B. 1937. “La prévision: Ses lois logiques, ses sources subjectives.” Annales de l’Institut Henri Poincaré 7:1–68.Google Scholar
Douven, I. 2013. “Inference to the Best Explanation, Dutch Books, and Inaccuracy Minimization.” Philosophical Quarterly 63 (252): 428–44..CrossRefGoogle Scholar
Eberhardt, F., and Danks, D.. 2011. “Confirmation in the Cognitive Sciences: The Problematic Case of Bayesian Models.” Minds and Machines 21 (3): 389–410..CrossRefGoogle Scholar
Estes, W. K. 1959. “The Statistical Approach to Learning.” In Psychology: A Study of a Science, Vol. 2, ed. S. Koch, 380–491. New York: McGraw-Hill.Google Scholar
Feynman, R. P. 1998. Lectures on Computation. Boston: Addison-Wesley.Google Scholar
Frank, M. C., and Goodman, N. D.. 2016. “Pragmatic Language Interpretation as Probabilistic Inference.” Trends in Cognitive Science 20:818–29.Google Scholar
Friston, K. 2010. “The Free-Energy Principle: A Unified Brain Theory?” Nature Reviews Neuroscience 11:127–38.CrossRefGoogle ScholarPubMed
Geisler, W. S., and Diehl, R. L.. 2002. “Bayesian Natural Selection and the Evolution of Perceptual Systems.” Philosophical Transactions of the Royal Society of London B 357:419–48.Google ScholarPubMed
Gigerenzer, G. 1991. “Does the Environment Have the Same Structure as Bayes’ Theorem?” Behavioral and Brain Sciences 14:495–96.CrossRefGoogle Scholar
Gigerenzer, G., and Brighton, H.. 2009. “Homo Heuristicus: Why Biased Minds Make Better Inferences.” Topics in Cognitive Science 1:107–43.CrossRefGoogle ScholarPubMed
Godfrey-Smith, P. 1996. Complexity and the Function of Mind in Nature. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Good, I. J. 1971. “46656 Varieties of Bayesians.” American Statistician 25:62–63.Google Scholar
Green, D. M., and Swets, J. A.. 1966. Signal Detection Theory and Psychophysics. New York: Wiley.Google Scholar
Griffiths, T. L., Lieder, F., and Goodman, N. D.. 2015. “Rational Use of Cognitive Resources: Levels of Analysis between the Computational and the Algorithmic.” Topics in Cognitive Science 7 (2): 217–29..CrossRefGoogle ScholarPubMed
Griffiths, T. L., and Tenenbaum, J. B.. 2006. “Optimal Predictions in Everyday Cognition.” Psychological Science 17 (9): 767–73..CrossRefGoogle ScholarPubMed
Hemmer, P., Tauber, S., and Steyvers, M.. 2015. “Moving beyond Qualitative Evaluations of Bayesian Models of Cognition.” Psychonomic Bulletin and Review 22 (3): 614–28..CrossRefGoogle ScholarPubMed
Huttegger, S. M. 2013. “In Defense of Reflection.” Philosophy of Science 80 (3): 413–33..CrossRefGoogle Scholar
Icard, T. F. 2013. “The Algorithmic Mind: A Study of Inference in Action.” PhD diss., Stanford University.Google Scholar
Icard, T. F. 2014. “Toward Boundedly Rational Analysis.” In Proceedings of the 36th Annual Meeting of the Cognitive Science Society, ed. Bello, P., Guarini, M., McShane, M., and Scassellati, B., 637–42. Red Hook, NY: Curran.Google Scholar
Bello, P., Guarini, M., McShane, M., and Scassellati, B. 2016. “Subjective Probability as Sampling Propensity.” Review of Philosophy and Psychology 7 (4): 863–903..Google Scholar
Jaynes, E. T. 1957. “Information Theory and Statistical Mechanics.” Physical Review 106 (4): 620–30..CrossRefGoogle Scholar
Jones, M., and Love, B. C.. 2011. “Bayesian Fundamentalism or Enlightenment? On the Explanatory Status and Theoretical Contributions of Bayesian Models of Cognition.” Behavioral and Brain Sciences 34 (4): 169–231..CrossRefGoogle ScholarPubMed
Kitcher, P. 1987. “Why Not the Best?” In The Latest on the Best, ed. Dupré, J., 77–102. Cambridge, MA: MIT Press.Google Scholar
Kwisthout, J., Wareham, T., and van Rooij, I.. 2008. “Bayesian Intractability Is Not an Ailment That Approximation Can Cure.” Cognitive Science 35:779–84.Google Scholar
Lewis, R. L., Howes, A., and Singh, S.. 2014. “Computational Rationality: Linking Mechanism and Behavior through Bounded Utility Maximization.” Topics in Cognitive Science 6 (2): 279–311..CrossRefGoogle ScholarPubMed
Luce, R. D. 1963. “Detection and Recognition.” In Handbook of Mathematical Psychology, ed. Luce, R. D., Bush, R. R., and Galanter, E., 103–89. New York: Wiley.Google Scholar
MacKay, D. 2003. Information Theory, Inference, and Learning Algorithms. Cambridge: Cambridge University Press.Google Scholar
Marcus, G. F., and Davis, E.. 2013. “How Robust Are Probabilistic Models of Higher-Level Cognition?” Psychological Science 24 (12): 2351–60..CrossRefGoogle ScholarPubMed
Mark, J. T., Marion, B. B., and Hoffman, D. D.. 2010. “Natural Selection and Veridical Perceptions.” Journal of Theoretical Biology 266:504–15.CrossRefGoogle ScholarPubMed
Marr, D. 1982. Vision. San Francisco: Freeman.Google Scholar
Mattsson, L.-G., and Weibull, J. W.. 2002. “Probabilistic Choice and Procedurally Bounded Rationality.” Games and Economic Behavior 41:61–78.CrossRefGoogle Scholar
Murphy, G. L. 1993. “A Rational Theory of Concepts.” Psychology of Learning and Motivation 29:327–59.CrossRefGoogle Scholar
Niven, J. E., and Laughlin, S. B.. 2008. “Energy Limitation as a Selective Pressure on the Evolution of Sensory Systems.” Journal of Experimental Biology 211:1792–1804.CrossRefGoogle ScholarPubMed
Oaksford, M., and Chater, N.. 2007. Bayesian Rationality. Oxford: Oxford University Press.CrossRefGoogle Scholar
Okasha, S. 2013. “The Evolution of Bayesian Updating.” Philosophy of Science 80:745–57.CrossRefGoogle Scholar
Ortega, P. A., and Braun, D. A.. 2013. “Thermodynamics as a Theory of Decision-Making with Information-Processing Costs.” Proceedings of the Royal Society of London A 469 (2153). doi:10.1098/rspa.2012.0683.CrossRefGoogle Scholar
Parker, G. A., and Smith, J. Maynard. 1990. “Optimality Theory in Evolutionary Biology.” Nature 348:27–33.CrossRefGoogle Scholar
Perfors, A., Tenenbaum, J. B., Griffiths, T. L., and Xu, F.. 2011. “A Tutorial Introduction to Bayesian Models of Cognitive Development.” Cognition 120:302–21.CrossRefGoogle ScholarPubMed
Peterson, C. R., and Beach, L. R.. 1967. “Man as an Intuitive Statistician.” Psychological Bulletin 68 (1): 29–46..CrossRefGoogle Scholar
Pylyshyn, Z. W. 1984. Computation and Cognition. Cambridge, MA: MIT Press.Google Scholar
Russell, S., and Subramanian, D.. 1995. “Provably Bounded-Optimal Agents.” Journal of Artificial Intelligence Research 2:1–36.CrossRefGoogle Scholar
Sanborn, A. N., Griffiths, T. L., and Shiffrin, R. M.. 2010. “Uncovering Mental Representations with Markov Chain Monte Carlo.” Cognitive Psychology 60:63–100.CrossRefGoogle ScholarPubMed
Sengupta, B., Stemmler, M. B., and Friston, K. J.. 2013. “Information and Efficiency in the Nervous System: A Synthesis.” PLoS Computational Biology 9 (7): 1–12..CrossRefGoogle ScholarPubMed
Simon, H. A. 1956. “Rational Choice and the Structure of the Environment.” Psychological Review 63 (2): 129–38..CrossRefGoogle ScholarPubMed
Simon, H. A. 1976. “From Substantive to Procedural Rationality.” In 25 Years of Economic Theory, ed. Kastelein, T. J., Kuipers, S. K., Nijenhuis, W. A., and Wagenaar, G. R., 65–86. Dordrecht: Springer.CrossRefGoogle Scholar
Kastelein, T. J., Kuipers, S. K., Nijenhuis, W. A., and Wagenaar, G. R. 1991. “Cognitive Architectures and Rational Analysis: Comment.” In Architectures for Intelligence: The 22nd Carnegie Mellon Symposium on Cognition, ed. VanLehn, K., 25–39. Mahwah, NJ: Erlbaum.Google Scholar
Sober, E. 2001. “The Two Faces of Fitness.” In Thinking about Evolution, Vol. 2, ed. R. S. Singh, C. B. Krimbas, D. B. Paul, and J. Beatty, 309–21. Cambridge: Cambridge University Press.Google Scholar
Stich, S. P. 1990. The Fragmentation of Reason. Cambridge, MA: MIT Press.Google Scholar
Sutton, R. S., and Barto, A. G.. 1998. Reinforcement Learning. Cambridge, MA: MIT Press.Google Scholar
Tenenbaum, J. T., Kemp, C., Griffiths, T., and Goodman, N. D.. 2011. “How to Grow a Mind: Statistics, Structure, and Abstraction.” Science 331:1279–85.CrossRefGoogle Scholar
Vul, E., Goodman, N. D., Griffiths, T. L., and Tenenbaum, J. B.. 2014. “One and Done? Optimal Decisions from Very Few Samples.” Cognitive Science 38 (4): 599–637..CrossRefGoogle ScholarPubMed