Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-31T19:20:25.527Z Has data issue: false hasContentIssue false

3 - Bayesian Models of Cognition

from Part II - Cognitive Modeling Paradigms

Published online by Cambridge University Press:  21 April 2023

By
Thomas L. Griffiths ,
Charles Kemp  and
Joshua B. Tenenbaum
Edited by
Ron Sun
Ron Sun
Affiliation:
Rensselaer Polytechnic Institute, New York
Get access

Summary

Many of the problems that human minds need to solve – including learning concepts, causal relationships, and languages – require making informed inferences from limited data. Bayesian models of cognition consider how an ideal agent should solve these problems, drawing on ideas from probability theory, statistics, machine learning, and artificial intelligence.  The resulting models can then be used to understand human behavior, identifying in formal terms the knowledge that human minds draw on when solving these problems and identifying potential mechanisms by which their solutions might be implemented. This chapter provides an introduction to Bayesian models of cognition, starting with the basic principles of probability theory and then considering more advanced topics such as graphical models, causal learning, hierarchical Bayesian models, and Markov chain Monte Carlo. The chapter ends with a brief review of recent theoretical developments.

Keywords

Bayesian modelscognitionlearninginferenceprobabilitystatistics
Type
Chapter
Information
The Cambridge Handbook of Computational Cognitive Sciences , pp. 80 - 138
Publisher: Cambridge University Press
Print publication year: 2023

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.)

References

Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. (1985). A learning algorithm for Boltzmann machines. Cognitive Science, 9, 147–169.Google Scholar
Anderson, J. R. (1990). The Adaptive Character of Thought. Hillsdale, NJ: Erlbaum.Google Scholar
Ashby, F. G., & Alfonso-Reese, L. A. (1995). Categorization as probability density estimation. Journal of Mathematical Psychology, 39, 216–233.Google Scholar
Atran, S. (1998). Folk biology and the anthropology of science: cognitive universals and cultural particulars. Behavioral and Brain Sciences, 21, 547–609.CrossRefGoogle ScholarPubMed
Bayes, T. (1763/1958). Studies in the history of probability and statistics: IX. Thomas Bayes’s essay towards solving a problem in the doctrine of chances. Biometrika, 45, 296–315.Google Scholar
Bernardo, J. M., & Smith, A. F. M. (1994). Bayesian Theory. New York, NY: Wiley.Google Scholar
Bishop, C. M. (2006). Pattern Recognition and Machine Learning. New York, NY: Springer.Google Scholar
Blei, D., Griffiths, T., Jordan, M., & Tenenbaum, J. (2004). Hierarchical topic models and the nested Chinese restaurant process. In Thrun, S., Saul, L. K., & Schölkopf, B. (Eds.), Advances in Neural Information Processing Systems 16. Cambridge, MA: MIT Press.Google Scholar
Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet Allocation. Journal of Machine Learning Research, 3, 993–1022.Google Scholar
Boas, M. L. (1983). Mathematical Methods in the Physical Sciences (2nd ed.). New York, NY: Wiley.Google Scholar
Bonawitz, E., Denison, S., Griffiths, T. L., & Gopnik, A. (2014). Probabilistic models, learning algorithms, and response variability: sampling in cognitive development. Trends in Cognitive Sciences, 18(10), 497–500.Google Scholar
Bowers, J. S., & Davis, C. J. (2012). Bayesian just-so stories in psychology and neuroscience. Psychological Bulletin, 138, 389–414.CrossRefGoogle ScholarPubMed
Brainard, D. H., & Freeman, W. T. (1997). Bayesian color constancy. Journal of the Optical Society of America A, 14, 1393–1411.CrossRefGoogle ScholarPubMed
Buehner, M., & Cheng, P. W. (1997). Causal induction: the Power PC theory versus the Rescorla-Wagner theory. In Shafto, M. & Langley, P. (Eds.), Proceedings of the 19th Annual Conference of the Cognitive Science Society (pp. 55–61). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
Buehner, M. J., Cheng, P. W., & Clifford, D. (2003). From covariation to causation: a test of the assumption of causal power. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 1119–1140.Google ScholarPubMed
Carey, S. (1985). Conceptual Change in Childhood. Cambridge, MA: MIT Press.Google Scholar
Charniak, E. (1993). Statistical Language Learning. Cambridge, MA: MIT Press.Google Scholar
Chater, N., Zhu, J.-Q., Spicer, J., Sundh, J., León-Villagrá, P., & Sanborn, A. (2020). Probabilistic biases meet the Bayesian brain. Current Directions in Psychological Science, 29(5), 506–512.CrossRefGoogle Scholar
Cheng, P. (1997). From covariation to causation: a causal power theory. Psychological Review, 104, 367–405.Google Scholar
Clark, A. (2015). Surfing Uncertainty: Prediction, Action, and the Embodied Mind. Oxford: Oxford University Press.Google Scholar
Collins, A. M., & Loftus, E. F. (1975). A spreading activation theory of semantic processing. Psychological Review, 82, 407–428.Google Scholar
Collins, A. M., & Quillian, M. R. (1969). Retrieval time from semantic memory. Journal of Verbal Learning and Verbal Behaviour, 8, 240–247.CrossRefGoogle Scholar
Dasgupta, I., Schulz, E., Tenenbaum, J. B., & Gershman, S. J. (2020). A theory of learning to infer. Psychological Review, 127(3), 412.Google Scholar
Davis, Z. J., Bramley, N. R., & Rehder, B. (2020). Causal structure learning in continuous systems. Frontiers in Psychology, 11, 244.CrossRefGoogle ScholarPubMed
Denison, S., Bonawitz, E., Gopnik, A., & Griffiths, T. L. (2013). Rational variability in children’s causal inferences: the sampling hypothesis. Cognition, 126(2), 285–300.Google Scholar
Duda, R. O., Hart, P. E., & Stork, D. G. (2000). Pattern Classification. New York, NY: Wiley.Google Scholar
Finn, C., Abbeel, P., & Levine, S. (2017). Model-agnostic meta-learning for fast adaptation of deep networks. arXiv preprint arXiv:1703.03400Google Scholar
Friedman, N., & Koller, D. (2000). Being Bayesian about network structure. In Proceedings of the 16th Annual Conference on Uncertainty in AI (pp. 201–210). Stanford, CA.Google Scholar
Friston, K., & Dolan, R. J. (2017). Computational psychiatry and the Bayesian brain. In Charney, D. S., Nestler, E. J., & Pamela Sklar, M. (Eds.), Charney & Nestler’s Neurobiology of Mental Illness. Oxford: Oxford University Press.Google Scholar
Froyen, V., Feldman, J., & Singh, M. (2015). Bayesian hierarchical grouping: perceptual grouping as mixture estimation. Psychological Review, 122(4), 575.CrossRefGoogle ScholarPubMed
Gal, Y., & Ghahramani, Z. (2016). Dropout as a Bayesian approximation: representing model uncertainty in deep learning. In the International Conference on Machine Learning (pp. 1050–1059).Google Scholar
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian Data Analysis. New York, NY: Chapman & Hall.Google Scholar
Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.CrossRefGoogle ScholarPubMed
Gershman, S., Vul, E., & Tenenbaum, J. (2009). Perceptual multistability as Markov chain Monte Carlo inference. Advances in Neural Information Processing Systems, 22, 611–619.Google Scholar
Gershman, S. J., Horvitz, E. J., & Tenenbaum, J. B. (2015). Computational rationality: a converging paradigm for intelligence in brains, minds, and machines. Science, 349(6245), 273–278.Google Scholar
Ghahramani, Z. (2004). Unsupervised learning. In Bousquet, O., Raetsch, G., & von Luxburg, U. (Eds.), Advanced Lectures on Machine Learning. Berlin: Springer-Verlag.Google Scholar
Gigerenzer, G., Swijtink, Z., Porter, T., Daston, L., Beatty, J., & Kruger, L. (1989). The Empire of Chance. Cambridge: Cambridge University Press.Google Scholar
Gilks, W., Richardson, S., & Spiegelhalter, D. J. (Eds.). (1996). Markov Chain Monte Carlo in Practice. Suffolk: Chapman and Hall.Google Scholar
Glassen, T., & Nitsch, V. (2016). Hierarchical Bayesian models of cognitive development. Biological Cybernetics, 110(2–3), 217–227.Google Scholar
Glymour, C. (2001). The Mind’s Arrows: Bayes Nets and Graphical Causal Models in Psychology. Cambridge, MA: MIT Press.Google Scholar
Glymour, C., & Cooper, G. (1999). Computation, Causation, and Discovery. Cambridge, MA: MIT Press.Google Scholar
Goldstein, H. (2003). Multilevel Statistical Models (3rd ed.). London: Hodder Arnold.Google Scholar
Good, I. J. (1980). Some history of the hierarchical Bayesian methodology. In Bernardo, J. M., DeGroot, M. H., Lindley, D. V., & Smith, A. F. M. (Eds.), Bayesian Statistics (pp. 489–519). Valencia: Valencia University Press.Google Scholar
Goodman, N. D., & Frank, M. C. (2016). Pragmatic language interpretation as probabilistic inference. Trends in Cognitive Sciences, 20(11), 818–829.CrossRefGoogle ScholarPubMed
Goodman, N. D., Frank, M. C., Griffiths, T. L., Tenenbaum, J. B., Battaglia, P. W., & Hamrick, J. B. (2015). Relevant and robust: a response to Marcus and Davis (2013). Psychological Science, 26(4), 539–541.Google Scholar
Goodman, N. D., Ullman, T. D., & Tenenbaum, J. B. (2011). Learning a theory of causality. Psychological Review, 118, 110–119.Google Scholar
Gopnik, A., & Meltzoff, A. N. (1997). Words, Thoughts, and Theories. Cambridge, MA: MIT Press.Google Scholar
Grant, E., Finn, C., Levine, S., Darrell, T., & Griffiths, T. (2018). Recasting gradient-based meta-learning as hierarchical bayes. arXiv preprint arXiv:1801.08930Google Scholar
Griffiths, T. L. (2020). Understanding human intelligence through human limitations. Trends in Cognitive Sciences, 24(11), 873–883.CrossRefGoogle ScholarPubMed
Griffiths, T. L., Chater, N., Norris, D., & Pouget, A. (2012). How the Bayesians got their beliefs (and what those beliefs actually are): comment on Bowers and Davis (2012). Psychological Bulletin, 138(3), 415–422.Google Scholar
Griffiths, T. L., Kemp, C., & Tenenbaum, J. B. (2008). Bayesian models of cognition. In Sun, R. (Ed.), Cambridge Handbook of Computational Cognitive Modeling. Cambridge: Cambridge University Press.Google Scholar
Griffiths, T. L., Lieder, F., & Goodman, N. D. (2015). Rational use of cognitive resources: levels of analysis between the computational and the algorithmic. Topics in Cognitive Science, 7(2), 217–229.Google Scholar
Griffiths, T. L., & Pacer, M. (2011). A rational model of causal inference with continuous causes. In Leen, T. K. (Ed.), Advances in Neural Information Processing Systems (pp. 2384–2392). Cambridge, MA: MIT Press.Google Scholar
Griffiths, T. L., & Steyvers, M. (2002). A probabilistic approach to semantic representation. In Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society. Hillsdale, NJ: Erlbaum.Google Scholar
Griffiths, T. L., & Steyvers, M. (2003). Prediction and semantic association. In Becker, S., Thrun, S., & Obermayer, K. (Eds.), Neural Information Processing Systems 15. Cambridge, MA: MIT Press.Google Scholar
Griffiths, T. L., & Steyvers, M. (2004). Finding scientific topics. Proceedings of the National Academy of Science, 101, 5228–5235.Google Scholar
Griffiths, T. L., Steyvers, M., Blei, D. M., & Tenenbaum, J. B. (2005). Integrating topics and syntax. In Saul, L. K., Weiss, Y., & Bottou, L. (Eds.), Advances in Neural Information Processing Systems 17. Cambridge, MA: MIT Press.Google Scholar
Griffiths, T. L., Steyvers, M., & Tenenbaum, J. B. (2007). Topics in semantic representation. Psychological Review, 114, 211–244.CrossRefGoogle ScholarPubMed
Griffiths, T. L., & Tenenbaum, J. B. (2005). Structure and strength in causal induction. Cognitive Psychology, 51, 354–384.Google Scholar
Griffiths, T. L., & Tenenbaum, J. B. (2009). Theory-based causal induction. Psychological Review, 116, 661–716.Google Scholar
Griffiths, T. L., Vul, E., & Sanborn, A. N. (2012). Bridging levels of analysis for probabilistic models of cognition. Current Directions in Psychological Science, 21, 263–268.Google Scholar
Hacking, I. (1975). The Emergence of Probability. Cambridge: Cambridg University Press.Google Scholar
Hagmayer, Y., & Mayrhofer, R. (2013). Hierarchical Bayesian models as formal models of causal reasoning. Argument & Computation, 4(1), 36–45.CrossRefGoogle Scholar
Hagmayer, Y., Sloman, S. A., Lagnado, D. A., & Waldmann, M. R. (2007). Causal reasoning through intervention. In A. Gopnik & L. Schulz (Eds.), Causal Learning: Psychology, Philosophy, and Computation. Oxford: Oxford University Press.Google Scholar
Hahn, U., & Oaksford, M. (2007). The rationality of informal argumentation: a Bayesian approach to reasoning fallacies. Psychological Review, 114(3), 704–732.Google Scholar
Hastings, W. K. (1970). Monte Carlo methods using Markov chains and their applications. Biometrika, 57, 97–109.Google Scholar
Heckerman, D. (1998). A tutorial on learning with Bayesian networks. In Jordan, M. I. (Ed.), Learning in Graphical Models (pp. 301–354). Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Heibeck, T., & Markman, E. (1987). Word learning in children: an examination of fast mapping. Child Development, 58, 1021–1024.Google Scholar
Hofmann, T. (1999). Probabilistic latent semantic indexing. In Proceedings of the Twenty-Second Annual International SIGIR Conference.Google Scholar
Holyoak, K. J., & Cheng, P. W. (2011). Causal learning and inference as a rational process: the new synthesis. Annual Review of Psychology, 62, 135–163.Google Scholar
Horvitz, E. J. (1990). Rational metareasoning and compilation for optimizing decisions under bounded resources (Tech. Rep.). Knowledge Systems Laboratory, Medical Computer Science, Stanford University, CA.Google Scholar
Huelsenbeck, J. P., & Ronquist, F. (2001). MRBAYES: Bayesian inference of phylogenetic trees. Bioinformatics, 17(8), 754–755.Google Scholar
Jeffreys, W. H., & Berger, J. O. (1992). Ockham’s razor and Bayesian analysis. American Scientist, 80(1), 64–72.Google Scholar
Jenkins, H. M., & Ward, W. C. (1965). Judgment of contingency between responses and outcomes. Psychological Monographs, 79(1), 1–17.Google Scholar
Jurafsky, D., & Martin, J. H. (2000). Speech and Language Processing. Upper Saddle River, NJ: Prentice Hall.Google Scholar
Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795.Google Scholar
Kemp, C., Perfors, A., & Tenenbaum, J. B. (2004). Learning domain structures. In Proceedings of the 26th Annual Conference of the Cognitive Science Society. Hillsdale, NJ: Erlbaum.Google Scholar
Kemp, C., Perfors, A., & Tenenbaum, J. B. (2007). Learning overhypotheses with hierarchical Bayesian models. Developmental Science, 10(3), 307–321.CrossRefGoogle ScholarPubMed
Kemp, C., & Tenenbaum, J. B. (2003). Theory-based induction. In Proceedings of the Twenty-Fifth Annual Conference of the Cognitive Science Society.Google Scholar
Kemp, C., Tenenbaum, J. B., Niyogi, S., & Griffiths, T. L. (2010). A probabilistic model of theory formation. Cognition, 114, 165–196.Google Scholar
Korb, K., & Nicholson, A. (2010). Bayesian Artificial Intelligence (2nd ed.). Boca Raton, FL: Chapman and Hall/CRC.Google Scholar
Lagnado, D., & Sloman, S. A. (2004). The advantage of timely intervention. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30, 856–876.Google ScholarPubMed
Landauer, T. K., & Dumais, S. T. (1997). A solution to Plato’s problem: the Latent Semantic Analysis theory of acquisition, induction, and representation of knowledge. Psychological Review, 104, 211–240.Google Scholar
LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436–444.CrossRefGoogle ScholarPubMed
Lee, M. D. (2006). A hierarchical Bayesian model of human decision-making on an optimal stopping problem. Cognitive Science, 30, 555–580.Google Scholar
Lieder, F., & Griffiths, T. L. (2020). Resource-rational analysis: understanding human cognition as the optimal use of limited computational resources. Behavioral and Brain Sciences, 43, e1.Google Scholar
Lieder, F., Griffiths, T. L., & Hsu, M. (2018). Overrepresentation of extreme events in decision making reflects rational use of cognitive resources. Psychological review, 125(1), 1.Google Scholar
Lieder, F., Griffiths, T. L., Huys, Q. J., & Goodman, N. D. (2018). The anchoring bias reflects rational use of cognitive resources. Psychonomic Bulletin & Review, 25(1), 322–349.CrossRefGoogle ScholarPubMed
Lu, H., Rojas, R. R., Beckers, T., & Yuille, A. L. (2016). A Bayesian theory of sequential causal learning and abstract transfer. Cognitive Science, 40(2), 404–439.Google Scholar
Lu, H., Yuille, A., Liljeholm, M., Cheng, P. W., & Holyoak, K. J. (2006). Modeling causal learning using Bayesian generic priors on generative and preventive powers. In Sun, R. & Miyake, N. (Eds.), Proceedings of the Twenty-Eighth Annual Conference of the Cognitive Science Society (pp. 519–524). Mahwah, NJ: Erlbaum.Google Scholar
Lu, H., Yuille, A., Liljeholm, M., Cheng, P. W., & Holyoak, K. J. (2007). Bayesian models of judgments of causal strength: a comparison. In McNamara, D. S. & Trafton, G. (Eds.), Proceedings of the Twenty-Eighth Annual Conference of the Cognitive Science Society (pp. 1241–1246). Mahwah, NJ: Erlbaum.Google Scholar
Lu, H., Yuille, A. L., Liljeholm, M., Cheng, P. W., & Holyoak, K. J. (2008). Bayesian generic priors for causal learning. Psychological Review, 115(4), 955–984.CrossRefGoogle ScholarPubMed
Lucas, C. G., & Griffiths, T. L. (2010). Learning the form of causal relationships using hierarchical Bayesian models. Cognitive Science, 34, 113–147.Google Scholar
Lund, K., & Burgess, C. (1996). Producing high-dimensional semantic spaces from lexical co-occurrence. Behavior Research Methods, Instrumentation, and Computers, 28, 203–208.Google Scholar
Mackay, D. J. C. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge: Cambridge University Press.Google Scholar
Mandelbaum, E. (2019). Troubles with Bayesianism: an introduction to the psychological immune system. Mind & Language, 34(2), 141–157.CrossRefGoogle Scholar
Manning, C., & Schütze, H. (1999). Foundations of Statistical Natural Language Processing. Cambridge, MA: MIT Press.Google Scholar
Mansinghka, V. K., Kemp, C., Tenenbaum, J. B., & Griffiths, T. L. (2006). Structured priors for structure learning. In Proceedings of the 22nd Conference on Uncertainty in Artificial Intelligence (UAI).Google Scholar
Marcus, G. F., & Davis, E. (2013). How robust are probabilistic models of higher-level cognition? Psychological Science, 24(12), 2351–2360.Google Scholar
Marr, D. (1982). Vision. San Francisco, CA: W. H. Freeman.Google Scholar
Medin, D. L., & Schaffer, M. M. (1978). Context theory of classification learning. Psychological Review, 85, 207–238.Google Scholar
Metropolis, A. W., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.Google Scholar
Minka, T., & Lafferty, J. (2002). Expectation-Propagation for the generative aspect model. In Proceedings of the 18th Conference on Uncertainty in Artificial Intelligence (UAI). San Francisco, CA: Morgan Kaufmann.Google Scholar
Myung, I. J., Forster, M. R., & Browne, M. W. (2000). Model selection [special issue]. Journal of Mathematical Psychology, 44, 1–2.Google Scholar
Myung, I. J., & Pitt, M. A. (1997). Applying Occam’s razor in modeling cognition: a Bayesian approach. Psychonomic Bulletin and Review, 4, 79–95.CrossRefGoogle Scholar
Navarro, D. J., & Kemp, C. (2017). None of the above: a Bayesian account of the detection of novel categories. Psychological Review, 124(5), 643–677.Google Scholar
Neal, R. M. (1993). Probabilistic inference using Markov chain Monte Carlo methods (Tech. Rep. No. CRG-TR-93-1). Toronto, University of Toronto.Google Scholar
Nelson, D. L., McEvoy, C. L., & Schreiber, T. A. (1998). The university of south florida word association, rhyme, and word fragment norms. Available from: http://w3.usf.edu/FreeAssociation/ [last accessed August 9, 2022].Google Scholar
Newman, M. E. J., & Barkema, G. T. (1999). Monte Carlo Methods in Statistical Physics. Oxford: Clarendon Press.Google Scholar
Nisbett, R. E., Krantz, D. H., Jepson, C., & Kunda, Z. (1983). The use of statistical heuristics in everyday inductive reasoning. Psychological Review, 90(4), 339–363.Google Scholar
Norris, D., & McQueen, J. M. (2008). Shortlist B: a Bayesian model of continuous speech recognition. Psychological Review, 115(2), 357.Google Scholar
Norris, J. R. (1997). Markov Chains. Cambridge: Cambridge University Press.Google Scholar
Nosofsky, R. M. (1986). Attention, similarity, and the identification-categorization relationship. Journal of Experimental Psychology: General, 115, 39–57.Google Scholar
Nosofsky, R. M. (1998). Optimal performance and exemplar models of classification. In Oaksford, M. & Chater, N. (Eds.), Rational Models of Cognition (pp. 218–247). Oxford: Oxford University Press.Google Scholar
Osherson, D. N., Smith, E. E., Wilkie, O., Lopez, A., & Shafir, E. (1990). Category-based induction. Psychological Review, 97(2), 185–200.Google Scholar
Pacer, M., & Griffiths, T. L. (2012). Elements of a rational framework for continuous-time causal induction. In Proceedings of the 34th Annual Conference of the Cognitive Science Society.Google Scholar
Pacer, M. D., & Griffiths, T. L. (2015). Upsetting the contingency table: causal induction over sequences of point events. In Proceedings of the 37th Annual Conference of the Cognitive Science Society.Google Scholar
Pajak, B., Fine, A. B., Kleinschmidt, D. F., & Jaeger, T. F. (2016). Learning additional languages as hierarchical probabilistic inference: insights from first language processing. Language Learning, 66(4), 900–944.Google Scholar
Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. San Francisco, CA: Morgan Kaufmann.Google Scholar
Pearl, J. (2000). Causality: Models, Reasoning and Inference. Cambridge: Cambridge University Press.Google Scholar
Pearl, J. (2018). The Book of Why: The New Science of Cause and Effect. New York, NY: Basic Books.Google Scholar
Pitman, J. (1993). Probability. New York, NY: Springer-Verlag.Google Scholar
Reed, S. K. (1972). Pattern recognition and categorization. Cognitive Psychology, 3, 393–407.Google Scholar
Rice, J. A. (1995). Mathematical Statistics and Data Analysis (2nd ed.). Belmont, CA: Duxbury.Google Scholar
Rips, L. J. (1975). Inductive judgments about natural categories. Journal of Verbal Learning and Verbal Behavior, 14, 665–681.Google Scholar
Russell, S. (1988). Analogy by similarity. In Helman, D. H. (Ed.), Analogical Reasoning (pp. 251–269). New York, NY: Kluwer Academic Publishers.Google Scholar
Russell, S. J., & Norvig, P. (2020). Artificial Intelligence: A Modern Approach (4th ed.). Saddle River, NJ: Pearson.Google Scholar
Sanborn, A. N., & Chater, N. (2016). Bayesian brains without probabilities. Trends in Cognitive Sciences, 20(12), 883–893.Google Scholar
Sanborn, A. N., Griffiths, T. L., & Navarro, D. J. (2010). Rational approximations to rational models: alternative algorithms for category learning. Psychological Review, 117, 1144–1167.Google Scholar
Shen, S., & Ma, W. J. (2016). A detailed comparison of optimality and simplicity in perceptual decision making. Psychological Review, 123(4), 452–480.Google Scholar
Shi, L., Griffiths, T. L., Feldman, N. H., & Sanborn, A. N. (2010). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin and Review, 17, 443–464.CrossRefGoogle ScholarPubMed
Shiffrin, R. M., & Steyvers, M. (1997). A model for recognition memory: REM: Retrieving Effectively from Memory. Psychonomic Bulletin & Review, 4, 145–166.Google Scholar
Sloman, S. (2005). Causal Models: How People Think About the World and Its Alternatives. Oxford: Oxford University Press.Google Scholar
Smith, L. B., Jones, S. S., Landau, B., Gershkoff-Stowe, L., & Samuelson, L. (2002). Object name learning provides on-the-job training for attention. Psychological Science, 13(1), 13–19.Google Scholar
Spirtes, P., Glymour, C., & Scheines, R. (1993). Causation Prediction and Search. New York, NY: Springer-Verlag.Google Scholar
Steyvers, M., Tenenbaum, J. B., Wagenmakers, E. J., & Blum, B. (2003). Inferring causal networks from observations and interventions. Cognitive Science, 27, 453–489.Google Scholar
Tauber, S., Navarro, D. J., Perfors, A., & Steyvers, M. (2017). Bayesian models of cognition revisited: setting optimality aside and letting data drive psychological theory. Psychological Review, 124(4), 410–441.Google Scholar
Tenenbaum, J. B., & Griffiths, T. L. (2001). Structure learning in human causal induction. In Leen, T., Dietterich, T., & Tresp, V. (Eds.), Advances in Neural Information Processing Systems 13 (pp. 59–65). Cambridge, MA: MIT Press.Google Scholar
Tenenbaum, J. B., Griffiths, T. L., & Kemp, C. (2006). Theory-based Bayesian models of inductive learning and reasoning. Trends in Cognitive Science, 10, 309–318.Google Scholar
Ullman, T. D., & Tenenbaum, J. B. (2020). Bayesian models of conceptual development: learning as building models of the world. Annual Review of Developmental Psychology, 2, 533–558.Google Scholar
Vul, E., Goodman, N., Griffiths, T. L., & Tenenbaum, J. B. (2014). One and done? Optimal decisions from very few samples. Cognitive Science, 38(4), 599–637.Google Scholar
Wellman, H. M., & Gelman, S. A. (1992). Cognitive development: foundational theories of core domains. Annual Review of Psychology, 43, 337–375.Google Scholar
Xu, F., & Kushnir, T. (2013). Infants are rational constructivist learners. Current Directions in Psychological Science, 22(1), 28–32.Google Scholar
Yeung, S., & Griffiths, T. L. (2015). Identifying expectations about the strength of causal relationships. Cognitive Psychology, 76, 1–29.Google Scholar
Yu, A. J. (2014). Bayesian models of attention. In Nobre, K., Nobre, A. C., & Kastner, S. (Eds.), The Oxford Handbook of Attention. Oxford: Oxford University Press.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×