Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-19T02:00:22.477Z Has data issue: false hasContentIssue false

Part VI - Computational Approaches

Published online by Cambridge University Press:  01 June 2023

Klaus Fiedler
Affiliation:
Universität Heidelberg
Peter Juslin
Affiliation:
Uppsala Universitet, Sweden
Jerker Denrell
Affiliation:
University of Warwick
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
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

References

Abbott, J. T., & Griffiths, T. L. (2011). Exploring the influence of particle filter parameters on order effects in causal learning. Proceedings of the Annual Meeting of the Cognitive Science Society, 33, 29502955.Google Scholar
Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174188.Google Scholar
Battaglia, P. W., Hamrick, J. B., & Tenenbaum, J. B. (2013). Simulation as an engine of physical scene understanding. Proceedings of the National Academy of Sciences, 110(45), 1832718332.Google Scholar
Blurton, S. P., Kyllingsbæk, S., Nielsen, C. S., & Bundesen, C. (2020). A Poisson random walk model of response times. Psychological Review, 127(3), 362.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), 497500.Google Scholar
Bowles, S., Kirman, A., & Sethi, R. (2017). Retrospectives: Friedrich Hayek and the market algorithm. Journal of Economic Perspectives, 31(3), 215–30.Google Scholar
Bramley, N. R., Dayan, P., Griffiths, T. L., & Lagnado, D. A. (2017). Formalizing Neurath’s ship: Approximate algorithms for online causal learning. Psychological Review, 124(3), 301.Google Scholar
Brown, G. D., Neath, I., & Chater, N. (2007). A temporal ratio model of memory. Psychological Review, 114(3), 539576.Google Scholar
Brown, S. D., & Steyvers, M. (2009). Detecting and predicting changes. Cognitive Psychology, 58(1), 4967.Google Scholar
Chater, N., & Manning, C. D. (2006). Probabilistic models of language processing and acquisition. Trends in Cognitive Sciences, 10(7), 335344.CrossRefGoogle ScholarPubMed
Dasgupta, I., Schulz, E., & Gershman, S. J. (2017). Where do hypotheses come from? Cognitive Psychology, 96, 125.CrossRefGoogle ScholarPubMed
Daw, N., & Courville, A. (2008). The pigeon as particle filter. Advances in Neural Information Processing Systems, 20, 369376.Google Scholar
Dellaportas, P., & Roberts, G. O. (2003). An introduction to MCMC. In Spatial statistics and computational methods (pp. 141). New York: Springer.Google Scholar
Doucet, A., De Freitas, N., & Gordon, N. (2001). An introduction to sequential Monte Carlo methods. In Sequential Monte Carlo methods in practice (pp. 3-14). New York: Springer.CrossRefGoogle Scholar
Earl, D. J., & Deem, M. W. (2005). Parallel tempering: Theory, applications, and new perspectives. Physical Chemistry Chemical Physics, 7(23), 39103916.CrossRefGoogle ScholarPubMed
Fox, C. R., & Tversky, A. (1998). A belief-based account of decision under uncertainty. Management Science, 44, 879895.CrossRefGoogle 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), 721741.Google Scholar
Gershman, S. J. (2019). Uncertainty and exploration. Decision, 6(3), 277.Google Scholar
Gershman, S. J., Blei, D. M., & Niv, Y. (2010). Context, learning, and extinction. Psychological Review, 117(1), 197.Google Scholar
Gershman, S. J., Vul, E., & Tenenbaum, J. B. (2012). Multistability and perceptual inference. Neural Computation, 24(1), 124.Google Scholar
Geweke, J. (1989). Bayesian inference in econometric models using Monte Carlo integration. Econometrica, 57(6), 13171339.Google Scholar
Geyer, C. J. (1991). Markov chain Monte Carlo maximum likelihood. In Keramidas, (Ed.), Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface. Interface Foundation, Fairfax Station, pp. 156–163.Google Scholar
Gilden, D. L. (2001). Cognitive emissions of 1/f noise. Psychological Review, 108(1), 33.Google Scholar
Gilden, D. L., Thornton, T., & Mallon, M. W. (1995). 1/f noise in human cognition. Science, 267(5205), 18371839.Google Scholar
Gittins, J., & Jones, D. (1979). A dynamic allocation index for the discounted multiarmed bandit problem. Biometrika. 66(3), 561565.CrossRefGoogle Scholar
Griffiths, T. L., & Tenenbaum, J. B. (2006). Optimal predictions in everyday cognition. Psychological Science, 17(9), 767773.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(4), 263268.CrossRefGoogle Scholar
Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3), 430454.Google Scholar
Koller, D., & Friedman, N. (2009). Probabilistic graphical models: principles and techniques. Cambridge; MA: MIT.Google Scholar
Krafft, P. M., Shmueli, E., Griffiths, T. L., & Tenenbaum, J. B. (2021). Bayesian collective learning emerges from heuristic social learning. Cognition, 212, 104469.Google Scholar
Kuhn, T. (1962). The structure of scientific revolutions, Chicago: University of Chicago Press.Google Scholar
Levy, R. P., Reali, F., & Griffiths, T. L. (2008). Modeling the effects of memory on human online sentence processing with particle filters. In Koller, D., Schuurmans, D., Bengio, Y., & Bottou, L. (Eds.), Advances in neural information processing systems 21 (pp. 937944).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
Lloyd, K., Sanborn, A., Leslie, D., & Lewandowsky, S. (2019). Why higher working memory capacity may help you learn: Sampling, search, and degrees of approximation. Cognitive Science, 43(12), e12805.Google Scholar
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6), 10871092.Google Scholar
Mosteller, F., & Nogee, P. (1951). An experimental measurement of utility. Journal of Political Economy, 59(5), 371404.CrossRefGoogle Scholar
Murphy, K. P. (2012). Machine learning: a probabilistic perspective. Cambridge, MA: MIT.Google Scholar
Nobandegani, A. S., Castanheira, K. D. S., Otto, A. R., & Shultz, T. R. (2018). Over-representation of extreme events in decision-making: A rational metacognitive account. arXiv preprint arXiv:1801.09848.Google Scholar
Osofsky, R. M. (1984). Choice, similarity, and the context theory of classification. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10(1), 104114.Google Scholar
Nosofsky, R. M. (2011). The generalized context model: An exemplar model of classification. In Pothos, E. M. & Wills, A. J. (Eds.), Formal approaches in categorization (pp. 1839). Cambridge University Press.Google Scholar
O’Hagan, A., & Forster, J. J. (2004). Kendall’s advanced theory of statistics: Bayesian inference (Vol. 2B). London: Arnold.Google Scholar
Pleskac, T. J., & Busemeyer, J. R. (2010). Two-stage dynamic signal detection: a theory of choice, decision time, and confidence. Psychological Review, 117(3), 864.CrossRefGoogle ScholarPubMed
Prat-Carrabin, A., Wilson, R. C., Cohen, J. D., & Azeredo da Silveira, R. (2021). Human inference in changing environments with temporal structure. Psychological Review, 128(5), 879912.CrossRefGoogle ScholarPubMed
Raaijmakers, J. G., & Shiffrin, R. M. (1981). Search of associative memory. Psychological Review, 88(2), 93134.CrossRefGoogle Scholar
Ratcliff, R., & Rouder, J. N. (1998). Modeling response times for two-choice decisions. Psychological Science, 9(5), 347356.Google Scholar
Rhodes, T., & Turvey, M. T. (2007). Human memory retrieval as Lévy foraging. Physica A: Statistical Mechanics and its Applications, 385(1), 255260.CrossRefGoogle Scholar
Roth, D. (1996). On the hardness of approximate reasoning. Artificial Intelligence, 82(1–2), 273302.CrossRefGoogle Scholar
Russo, D. J., Van Roy, B., Kazerouni, A., Osband, I., & Wen, Z. (2018). A tutorial on Thompson sampling. Foundations and Trends® in Machine Learning, 11(1), 196.Google Scholar
Sanborn, A. N., & Chater, N. (2016). Bayesian brains without probabilities. Trends in Cognitive Sciences, 20(12), 883893.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(4), 1144.CrossRefGoogle ScholarPubMed
Sanborn, A. N., Mansinghka, V. K., & Griffiths, T. L. (2013). Reconciling intuitive physics and Newtonian mechanics for colliding objects. Psychological Review, 120(2), 411.Google Scholar
Shadlen, M. N., & Shohamy, D. (2016). Decision making and sequential sampling from memory. Neuron, 90(5), 927939.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 & Review, 17(4), 443464.Google Scholar
Sloman, S., Rottenstreich, Y., Wisniewski, E., Hadjichristidis, C., & Fox, C. R. (2004). Typical versus atypical unpacking and superadditive probability judgment. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30, 573582.Google Scholar
Speekenbrink, M. (2016). A tutorial on particle filters. Journal of Mathematical Psychology, 73, 140152.Google Scholar
Speekenbrink, M., & Konstantinidis, E. (2015). Uncertainty and exploration in a restless bandit problem. Topics in Cognitive Science, 7(2), 351367.Google Scholar
Spicer, J., Mullett, T. L., & Sanborn, A. N. (2022, December 2). Repeated Risky Choices Become More Consistent with Themselves but not Expected Value, with No Effect of Trial Order. https://doi.org/10.31234/osf.io/jgefrCrossRefGoogle Scholar
Stigler, S. M. (1986). The history of statistics: The measurement of uncertainty before 1900. Cambridge, MA: Harvard University Press.Google Scholar
Thompson, W. R. (1933). On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika, 25(3–4), 285294.CrossRefGoogle Scholar
Tierney, L. (1994). Markov chains for exploring posterior distributions. Annals of Statistics, 1701–1728.Google Scholar
Todd, P. M., & Hills, T. T. (2020). Foraging in mind. Current Directions in Psychological Science, 29(3), 309315.Google Scholar
Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5(2), 207232.CrossRefGoogle Scholar
Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. Psychological Review, 108(3), 550.CrossRefGoogle ScholarPubMed
Van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32(6), 939984.Google Scholar
Von Neumann, J., & Morgenstern, O. (2007). Theory of games and economic behavior (commemorative edition). Princeton: Princeton University Press.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), 599637.Google Scholar
Vul, E., & Pashler, H. (2008). Measuring the crowd within: Probabilistic representations within individuals. Psychological Science, 19(7), 645647.Google Scholar
Vulkan, N. (2000). An economist’s perspective on probability matching. Journal of Economic Surveys, 14(1), 101118.Google Scholar
Wagenaar, W. A. (1972). Generation of random sequences by human subjects: A critical survey of literature. Psychological Bulletin, 77(1), 6572.CrossRefGoogle Scholar
Wolpert, D. M. (2007). Probabilistic models in human sensorimotor control. Human Movement Science, 26(4), 511524.Google Scholar
Yi, M. S., Steyvers, M., & Lee, M. (2009). Modeling human performance in restless bandits with particle filters. Journal of Problem Solving, 2(2), 5.Google Scholar
Zhu, J.-Q., Sanborn, A., & Chater, N. (2018). Mental sampling in multimodal representations. Advances in Neural Information Processing Systems, 31, 57485759.Google Scholar

References

Anderson, J. R. (1990). The adaptive character of thought. Hillsdale, NJ: Psychology Press.Google Scholar
Anderson, J. R. (1991). The adaptive nature of human categorization. Psychological Review, 98(3), 409.Google Scholar
Baddeley, A. (1998). Random generation and the executive control of working memory. Quarterly Journal of Experimental Psychology: Section A, 51(4), 819852.Google Scholar
Battaglia, P. W., Hamrick, J. B., & Tenenbaum, J. B. (2013). Simulation as an engine of physical scene understanding. Proceedings of the National Academy of Sciences, 110(45), 1832718332.Google Scholar
Beaumont, M. A. (2019). Approximate Bayesian computation. Annual Review of Statistics and its Application, 6, 379403.Google Scholar
Bousfield, W. A., & Sedgewick, C. H. W. (1944). An analysis of sequences of restricted associative responses. Journal of General Psychology, 30(2), 149165.Google Scholar
Buesing, L., Bill, J., Nessler, B., & Maass, W. (2011). Neural dynamics as sampling: A model for stochastic computation in recurrent networks of spiking neurons. PLoS Computational Biology, 7(11), e1002211.Google Scholar
Castillo, L., León-Villagrá, P., Chater, N., & Sanborn, A. (2021). Local sampling with momentum accounts for human random sequence generation. Proceedings of the Annual Meeting of the Cognitive Science Society, 43. https://escholarship.org/uc/item/3gz154kgGoogle Scholar
Zhu, J.-Q., Spicer, J., Sanborn, A. N., & Chater, N. (Preprint). Cognitive variability matches speculative price dynamics. doi: 10.31234/osf.io/gfjvsGoogle Scholar
Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1(2), 223236Google Scholar
Correll, J. (2008). 1/f noise and effort on implicit measures of bias. Journal of Personality and Social Psychology, 94(1), 48.CrossRefGoogle ScholarPubMed
Costello, F., & Watts, P. (2014). Surprisingly rational: Probability theory plus noise explains biases in judgment. Psychological Review, 121(3), 463.Google Scholar
Dasgupta, I., Schulz, E., & Gershman, S. J. (2017). Where do hypotheses come from? Cognitive Psychology, 96, 125.Google Scholar
Edwards, W. (1968). Conservatism in human information processing: Formal representation of human judgment. Hoboken, NJ: John Wiley.Google Scholar
Erev, I., Wallsten, T. S., & Budescu, D. V. (1994). Simultaneous over-and underconfidence: The role of error in judgment processes. Psychological Review, 101(3), 519.Google Scholar
Fiser, J., Berkes, P., Orbán, G., & Lengyel, M. (2010). Statistically optimal perception and learning: From behavior to neural representations. Trends in Cognitive Sciences, 14(3), 119130.CrossRefGoogle ScholarPubMed
Gardner, M. (1978). White and brown music, fractal curves and one-over-f fluctuations. Scientific American, 238(4), 1627.Google Scholar
Gigerenzer, G., & Selten, R. (Eds.). (2002). Bounded rationality: The adaptive toolbox. Cambridge, MA: MIT.Google Scholar
Gilden, D. L. (1997). Fluctuations in the time required for elementary decisions. Psychological Science, 8(4), 296301.Google Scholar
Gilden, D. L., Thornton, T., & Mallon, M. W. (1995). 1/f noise in human cognition. Science, 267(5205), 18371839.Google Scholar
Hahn, U., & Oaksford, M. (2007). The rationality of informal argumentation: A Bayesian approach to reasoning fallacies. Psychological Review, 114(3), 704.Google Scholar
Hayes, B. K., Banner, S., Forrester, S., & Navarro, D. J. (2019). Selective sampling and inductive inference: Drawing inferences based on observed and missing evidence. Cognitive Psychology, 113, 101221.Google Scholar
Hilbert, M. (2012). Toward a synthesis of cognitive biases: How noisy information processing can bias human decision making. Psychological Bulletin, 138(2), 211.Google Scholar
Hills, T. T., Jones, M. N., & Todd, P. M. (2012). Optimal foraging in semantic memory. Psychological Review, 119(2), 431.Google Scholar
Howe, R., & Costello, F. (2020). Random variation and systematic biases in probability estimation. Cognitive Psychology, 123, 101306.Google Scholar
Hoyer, P. O., & Hyvärinen, A. (2003). Interpreting neural response variability as Monte Carlo sampling of the posterior. In Becker, S., Thrun, S. & Obermayer, K. (Eds.), Advances in neural information processing systems (pp. 293300). Cambridge, MA: MIT.Google Scholar
Juslin, P., Winman, A., & Hansson, P. (2007). The naïve intuitive statistician: A naïve sampling model of intuitive confidence intervals. Psychological Review, 114(3), 678703.Google Scholar
Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3), 430454.Google Scholar
Kersten, D., Mamassian, P., & Yuille, A. (2004). Object perception as Bayesian inference. Annual Review of Psychology, 55, 271304.Google Scholar
Koehler, D. J., & James, G. (2009). Probability matching in choice under uncertainty: Intuition versus deliberation. Cognition, 113(1), 123127.Google Scholar
Konovalova, E., & Le Mens, G. (2020). An information sampling explanation for the in-group heterogeneity effect. Psychological Review, 127(1), 47.Google Scholar
Lake, B. M., Salakhutdinov, R., & Tenenbaum, J. B. (2015). Human-level concept learning through probabilistic program induction. Science, 350(6266), 13321338.Google Scholar
Le Mens, G., & Denrell, J. (2011). Rational learning and information sampling: On the “naivety” assumption in sampling explanations of judgment biases. Psychological Review, 118(2), 379.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.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), 322349.Google Scholar
Lloyd, K., Sanborn, A., Leslie, D., & Lewandowsky, S. (2019). Why higher working memory capacity may help you learn: Sampling, search, and degrees of approximation. Cognitive Science, 43(12), e12805.Google Scholar
Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. Cambridge, MA: MIT.Google Scholar
Moreno-Bote, R., Knill, D. C., & Pouget, A. (2011). Bayesian sampling in visual perception. Proceedings of the National Academy of Sciences, 108(30), 1249112496.CrossRefGoogle ScholarPubMed
Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101(4), 608.CrossRefGoogle Scholar
Oaksford, M., & Chater, N. (2009). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.Google Scholar
Oaksford, M., & Chater, N. (2020). New paradigms in the psychology of reasoning. Annual Review of Psychology, 71, 305330.Google Scholar
Peterson, C. R., & Beach, L. R. (1967). Man as an intuitive statistician. Psychological Bulletin, 68(1), 29.Google Scholar
Redelmeier, D. A., Koehler, D. J., Liberman, V., & Tversky, A. (1995). Probability judgment in medicine: Discounting unspecified possibilities. Medical Decision Making, 15(3), 227230.Google Scholar
Reyna, V. F., & Lloyd, F. J. (2006). Physician decision making and cardiac risk: Effects of knowledge, risk perception, risk tolerance, and fuzzy processing. Journal of Experimental Psychology: Applied, 12(3), 179.Google Scholar
Rhodes, T., & Turvey, M. T. (2007). Human memory retrieval as Lévy foraging. Physica A: Statistical Mechanics and its Applications, 385(1), 255260.Google Scholar
Sanborn, A. N., & Chater, N. (2016). Bayesian brains without probabilities. Trends in Cognitive Sciences, 20(12), 883893.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(4), 1144.Google Scholar
Sanborn, A. N., Mansinghka, V. K., & Griffiths, T. L. (2013). Reconciling intuitive physics and Newtonian mechanics for colliding objects. Psychological Review, 120(2), 411.Google Scholar
Sanborn, A. N., Zhu, J.-Q., Spicer, J., et al. (2021). Sampling as the human approximation to probabilistic inference. In Muggleton, S. & Chater, N. (Eds). Human-like machine intelligence. Oxford: Oxford University Press.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 & Review, 17(4), 443464.Google Scholar
Simon, H. A. (1955). A behavioral model of rational choice. Quarterly Journal of Economics, 69(1), 99118.CrossRefGoogle Scholar
Sloman, S., Rottenstreich, Y., Wisniewski, E., Hadjichristidis, C., & Fox, C. R. (2004). Typical versus atypical unpacking and superadditive probability judgment. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30(3), 573.Google Scholar
Stewart, N., Chater, N., & Brown, G. D. (2006). Decision by sampling. Cognitive Psychology, 53(1), 126.Google Scholar
Sundh, J., Zhu, J. Q., Chater, N., & Sanborn, A. (2021, July 30). The mean-variance signature of Bayesian probability judgment. https://doi.org/10.31234/osf.io/yuhazGoogle Scholar
Tentori, K., Crupi, V., & Russo, S. (2013). On the determinants of the conjunction fallacy: Probability versus inductive confirmation. Journal of Experimental Psychology: General, 142(1), 235.Google Scholar
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 11241131.Google Scholar
Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90(4), 293.Google Scholar
Van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32(6), 939984.Google Scholar
Van Rooij, I., & Wareham, T. (2012). Intractability and approximation of optimization theories of cognition. Journal of Mathematical Psychology, 56(4), 232247.Google Scholar
Viswanathan, G. M., Buldyrev, S. V., Havlin, S., et al. (1999). Optimizing the success of random searches. Nature, 401(6756), 911914.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), 599637.Google Scholar
Wagenaar, W. A. (1972). Generation of random sequences by human subjects: A critical survey of literature. Psychological Bulletin, 77(1), 65.Google Scholar
Zhu, J.-Q., Leon-Villagra, P., Chater, N., & Sanborn, A. N. (2022). Understanding the structure of cognitive noise. PLOS Computational Biology, 18(8). doi: 10.1371/journal.pcbi.1010312Google Scholar
Zhu, J. Q., Sanborn, A. N., & Chater, N. (2018). Mental sampling in multimodal representations. In Bengio, S., Wallach, H., Larochelle, H. et al. (Eds.), Advances in neural information processing systems 31. Montreal: Curran Associates.Google Scholar
Zhu, J. Q., Sanborn, A., & Chater, N. (2019). Why decisions bias perception: An amortised sequential sampling account. Proceedings of the Annual Meeting of the Cognitive Science Society, 41, 32203226.Google Scholar
Zhu, J. Q., Sanborn, A. N., & Chater, N. (2020). The Bayesian sampler: Generic Bayesian inference causes incoherence in human probability judgments. Psychological Review, 127(5), 719748.Google Scholar
Zhu, J.-Q., Spicer, J., Sanborn, A. N., & Chater, N. (Preprint). Cognitive variability matches speculative price dynamics. doi: 10.31234/osf.io/gfjvsGoogle Scholar
Zhu, J., Sundh, J., Spicer, J., Chater, N., & Sanborn, A. N. (2021, February 4). The autocorrelated Bayesian sampler: A rational process for probability judgments, estimates, confidence intervals, choices, confidence judgments, and response times. https://doi.org/10.31234/osf.io/3qxf7Google Scholar

References

Adams, G. S., Converse, B. A., Hales, A. H., & Klotz, L. E. (2021). People systematically overlook subtractive changes. Nature, 592(7853), 258261.Google Scholar
Baker, C. L., Saxe, R., & Tenenbaum, J. B. (2009). Action understanding as inverse planning. Cognition, 113(3), 329349.Google Scholar
Bartlett, F. C. (1932). Remembering: A study in experimental and social psychology. Cambridge, UK: Cambridge University Press.Google Scholar
Battaglia, P. W., Hamrick, J. B., & Tenenbaum, J. B. (2013). Simulation as an engine of physical scene understanding. Proceedings of the National Academy of Sciences, 110(45), 1832718332.Google Scholar
Bogacz, R., Brown, E., Moehlis, J., Holmes, P., & Cohen, J. D. (2006). The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced-choice tasks. Psychological review, 113(4), 700.Google Scholar
Bonawitz, E., Denison, S., Gopnik, A., & Griffiths, T. L. (2014). Win-stay, lose-sample: A simple sequential algorithm for approximating Bayesian inference. Cognitive psychology, 74, 3565.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), 497500.Google Scholar
Bonawitz, E. B., & Griffiths, T. L. (2010). Deconfounding hypothesis generation and evaluation in Bayesian models. Proceedings of the Annual Meeting of the Cognitive Science Society, 32(32).Google Scholar
Bourgin, D., Abbott, J., Griffiths, T., Smith, K., & Vul, E. (2014). Empirical evidence for Markov chain Monte Carlo in memory search. Proceedings of the Annual Meeting of the Cognitive Science Society, 36(36).Google Scholar
Braddick, O. (1974). A short-range process in apparent motion. Vision Research, 14(7), 519527.Google Scholar
Chater, N., Tenenbaum, J. B., & Yuille, A. (2006). Probabilistic models of cognition: Where next? Trends in Cognitive Sciences, 10(7), 292293.Google Scholar
Chernev, A., Böckenholt, U., & Goodman, J. (2015). Choice overload: A conceptual review and meta-analysis. Journal of Consumer Psychology, 25(2), 333358.Google Scholar
Coenen, A., & Gureckis, T. (2021). The distorting effects of deciding to stop sampling information. PsyArXiv. doi:10.31234/osf.io/tbreaGoogle Scholar
Dasgupta, I., & Gershman, S. J. (2021). Memory as a computational resource. Trends in Cognitive Sciences, 25(3), 240251.Google Scholar
Dasgupta, I., Schulz, E., & Gershman, S. J. (2017). Where do hypotheses come from? Cognitive Psychology, 96, 125.Google Scholar
Dasgupta, I., Schulz, E., Goodman, N. D., & Gershman, S. J. (2018). Remembrance of inferences past: Amortization in human hypothesis generation. Cognition, 178, 6781.Google 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
Daw, N., & Courville, A. (2008). The pigeon as particle filter. Advances in Neural Information Processing Systems, 20, 369376.Google Scholar
Daw, N. D., O’Doherty, J. P., Dayan, P., Seymour, B., & Dolan, R. J. (2006). Cortical substrates for exploratory decisions in humans. Nature, 441(7095), 876879.Google Scholar
Dawes, R. M. (1993). Prediction of the future versus an understanding of the past: A basic asymmetry. American Journal of Psychology, 106(1), 1–24.Google Scholar
Denison, S., Bonawitz, E., Gopnik, A., & Griffiths, T. L. (2013). Rational variability in children’s causal inferences: The sampling hypothesis. Cognition, 126(2), 285300.Google Scholar
Doucet, A., de Freitas, N., & Gordon, N. (Eds.) (2001). Sequential Monte Carlo methods in practice. New York: Springer.Google Scholar
Fechner, G. T. (1860). Elemente der psychophysik (Vol. 2). Wiesbaden: Breitkopf u. Härtel.Google Scholar
Fiedler, K. (2000). Beware of samples! A cognitive-ecological sampling approach to judgment biases. Psychological Review, 107(4), 659.Google Scholar
Fiedler, K. (2008). The ultimate sampling dilemma in experience-based decision making. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34(1), 186.Google Scholar
Fiedler, K., & Juslin, P. (2006). Taking the interface between mind and environment seriously. In Fiedler, K. & Juslin, P. (Eds.), Information sampling and adaptive cognition (pp. 332). New York: Cambridge University Press.Google Scholar
Galesic, M., Olsson, H., & Rieskamp, J. (2012). Social sampling explains apparent biases in judgments of social environments. Psychological Science, 23(12), 15151523.Google Scholar
Galesic, M., Olsson, H., & Rieskamp, J. (2018). A sampling model of social judgment. Psychological Review, 125(3), 363.Google Scholar
Gershman, S., & Goodman, N. (2014). Amortized inference in probabilistic reasoning. Proceedings of the Annual Meeting of the Cognitive Science Society, 36(36).Google Scholar
Gershman, S., Horvitz, E. J., & Tenenbaum, J. B. (2015). Computational rationality: A converging paradigm for intelligence in brains, minds, and machines. Science, 349(6245), 273278.Google Scholar
Gershman, S. J., Vul, E., & Tenenbaum, J. B. (2012). Multistability and perceptual inference. Neural Computation, 24(1), 124.CrossRefGoogle ScholarPubMed
Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103(4), 650.Google Scholar
Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102(4), 684.Google Scholar
Gilks, W. R., Richardson, S., & Spiegelhalter, D. (1995). Markov chain Monte Carlo in practice. Boca Raton, FL: CRC Press.CrossRefGoogle Scholar
Gittins, J. C. (1979). Bandit processes and dynamic allocation indices. Journal of the Royal Statistical Society: Series B (Methodological), 41(2), 148164.Google Scholar
Gläscher, J., Daw, N., Dayan, P., & O’Doherty, J. P. (2010). States versus rewards: Dissociable neural prediction error signals underlying model-based and model-free reinforcement learning. Neuron, 66(4), 585595.Google Scholar
Goodman, N. D., Tenenbaum, J. B., Feldman, J., & Griffiths, T. L. (2008). A rational analysis of rule-based concept learning. Cognitive Science, 32(1), 108154.Google Scholar
Gopnik, A., Griffiths, T. L., & Lucas, C. G. (2015). When younger learners can be better (or at least more open-minded) than older ones. Current Directions in Psychological Science, 24(2), 8792.Google Scholar
Gopnik, A., O’Grady, S., & Lucas, C. G., et al. (2017). Changes in cognitive flexibility and hypothesis search across human life history from childhood to adolescence to adulthood. Proceedings of the National Academy of Sciences, 114(30), 78927899.Google Scholar
Griffiths, T. L., & Tenenbaum, J. B. (2006). Optimal predictions in everyday cognition. Psychological Science, 17(9), 767773.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(4), 263268.Google Scholar
Hau, R., Pleskac, T. J., & Hertwig, R. (2010). Decisions from experience and statistical probabilities: Why they trigger different choices than a priori probabilities. Journal of Behavioral Decision Making, 23(1), 4868.Google Scholar
Hauser, J. R., & Wernerfelt, B. (1990). An evaluation cost model of consideration sets. Journal of Consumer Research, 16(4), 393408.Google Scholar
Hayden, B., & Niv, Y. (2020). The case against economic values in the brain. Behavioral Neuroscience, 135(2), 192201.Google Scholar
Hertwig, R., Barron, G., Weber, E. U., & Erev, I. (2004). Decisions from experience and the effect of rare events in risky choice. Psychological Science, 15, 534539.Google Scholar
Hertwig, R., & Erev, I. (2009). The description–experience gap in risky choice. Trends in Cognitive Sciences, 13, 517523.Google Scholar
Hertwig, R., & Pleskac, T. J. (2010). Decisions from experience: Why small samples? Cognition, 115, 225237.Google Scholar
Hills, T. T., Jones, M. N., & Todd, P. M. (2012). Optimal foraging in semantic memory. Psychological Review, 119(2), 431.Google Scholar
Hogarth, R. M., Lejarraga, T., & Soyer, E. (2015). The two settings of kind and wicked learning environments. Current Directions in Psychological Science, 24(5), 379385.Google Scholar
Hourihan, K. L., & Benjamin, A. S. (2010). Smaller is better (when sampling from the crowd within): Low memory-span individuals benefit more from multiple opportunities for estimation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 36(4), 1068.Google Scholar
Jazayeri, M., & Movshon, J. A. (2007). A new perceptual illusion reveals mechanisms of sensory decoding. Nature, 446(7138), 912915.Google Scholar
Johnson, J. G., & Raab, M. (2003). Take the first: Option-generation and resulting choices. Organizational Behavior and Human Decision Processes, 91(2), 215229.Google Scholar
Jones, M., & 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.Google Scholar
Juni, M. Z., Gureckis, T. M., & Maloney, L. T. (2016). Information sampling behavior with explicit sampling costs. Decision, 3, 147.Google Scholar
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263292.Google Scholar
Kaiser, S., Simon, J. J., & Kalis, A., et al. (2013). The cognitive and neural basis of option generation and subsequent choice. Cognitive, Affective, & Behavioral Neuroscience, 13(4), 814829.Google Scholar
Kalis, A., Kaiser, S., & Mojzisch, A. (2013). Why we should talk about option generation in decision-making research. Frontiers in Psychology, 4, 555.Google Scholar
Karnopp, D. C. (1963). Random search techniques for optimization problems. Automatica, 1(2–3), 111121.Google Scholar
Klayman, J., & Ha, Y.-W. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94(2), 211.Google Scholar
Knill, D. C., & Richards, W. (1996). Perception as Bayesian inference. New York: Cambridge University Press.Google Scholar
Konovalova, E., & Le Mens, G. (2020). An information sampling explanation for the in-group heterogeneity effect. Psychological Review, 127(1), 47.Google Scholar
Kwisthout, J., Wareham, T., & van Rooij, I. (2011). Bayesian intractability is not an ailment that approximation can cure. Cognitive Science, 35(5), 779784.Google Scholar
Levy, R. P., Reali, F., & Griffiths, T. L. (2009). Modeling the effects of memory on human online sentence processing with particle filters. Advances in Neural Information Processing Systems, 21, 937944.Google Scholar
Lewandowsky, S., Griffiths, T. L., & Kalish, M. L. (2009). The wisdom of individuals: Exploring people’s knowledge about everyday events using iterated learning. Cognitive Science, 33(6), 969998.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.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), 322349.Google Scholar
Logan, G. D. (1988a). Toward an instance theory of automatization. Psychological Review, 95(4), 492.Google Scholar
Logan, G. D. (1988b). Toward an instance theory of automatization. Psychological Review, 95(4), 492.Google Scholar
Loomes, G., & Sugden, R. (1982). Regret theory: An alternative theory of rational choice under uncertainty. Economic Journal, 92(368), 805824.Google Scholar
Loomes, G., & Sugden, R. (1986). Disappointment and dynamic consistency in choice under uncertainty. Review of Economic Studies, 53(2), 271282.Google Scholar
Lucas, C. G., Bridgers, S., Griffiths, T. L., & Gopnik, A. (2014). When children are better (or at least more open-minded) learners than adults: Developmental differences in learning the forms of causal relationships. Cognition, 131(2), 284299.Google Scholar
Mellers, B. A., Schwartz, A., Ho, K., & Ritov, I. (1997). Decision affect theory: Emotional reactions to the outcomes of risky options. Psychological Science, 8(6), 423429.Google Scholar
Morris, A., Phillips, J., Huang, K., & Cushman, F. (2021). Generating options and choosing between them depend on distinct forms of value representation. Psychological Science, 32(11), 17311746.Google Scholar
Mozer, M. C., Pashler, H., & Homaei, H. (2008). Optimal predictions in everyday cognition: The wisdom of individuals or crowds? Cognitive Science, 32(7), 11331147.Google Scholar
Navarro, D. J., & Perfors, A. F. (2011). Hypothesis generation, sparse categories, and the positive test strategy. Psychological Review, 118(1), 120.Google Scholar
Nocedal, J., & Wright, S. (2006). Numerical optimization. New York: Springer Science & Business Media.Google Scholar
Nosofsky, R. M., & Palmeri, T. J. (1997). An exemplar-based random walk model of speeded classification. Psychological Review, 104(2), 266.Google Scholar
Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101(4), 608.Google Scholar
Oaksford, M., & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.Google Scholar
Pezzulo, G., Rigoli, F., & Chersi, F. (2013). The mixed instrumental controller: Using value of information to combine habitual choice and mental simulation. Frontiers in Psychology, 4, 92.Google Scholar
Phillips, J., Morris, A., & Cushman, F. (2019). How we know what not to think. Trends in Cognitive Sciences, 23, 10261040.Google Scholar
Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59.Google Scholar
Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. Neural Computation, 20(4), 873922.Google Scholar
Ratcliff, R., & Smith, P. L. (2004). A comparison of sequential sampling models for two-choice reaction time. Psychological Review, 111(2), 333.Google Scholar
Robert, C. P., & Casella, G. (1999). Monte Carlo statistical methods (Vol. 2). New York: Springer.Google Scholar
Rothe, A., Lake, B. M., & Gureckis, T. M. (2018). Do people ask good questions? Computational Brain & Behavior, 1, 6989.Google Scholar
Sanborn, A. N. (2017). Types of approximation for probabilistic cognition: Sampling and variational. Brain and Cognition, 112, 98101.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(4), 1144.Google Scholar
Savage, L. J. (1954). The foundations of statistics. New York: Wiley.Google Scholar
Schulz, E., Wu, C. M., Ruggeri, A., & Meder, B. (2019). Searching for rewards like a child means less generalization and more directed exploration. Psychological Science, 30(11), 15611572.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 & Review, 17(4), 443464.Google Scholar
Smaldino, P. E., & Richerson, P. J. (2012). The origins of options. Frontiers in Neuroscience, 6, 50.Google Scholar
Smith, K., Huber, D. E., & Vul, E. (2013). Multiply-constrained semantic search in the remote associates test. Cognition, 128(1), 6475.Google Scholar
Stewart, N., Chater, N., & Brown, G. D. (2006). Decision by sampling. Cognitive Psychology, 53, 126.Google Scholar
Tenenbaum, J. B., Kemp, C., Griffiths, T. L., & Goodman, N. D. (2011). How to grow a mind: Statistics, structure, and abstraction. Science, 331(6022), 12791285.Google Scholar
Thompson, W. R. (1933). On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika, 25(3/4), 285294.Google Scholar
Tversky, A., & Kahneman, D. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263291.Google Scholar
Ullman, T. D., Spelke, E., Battaglia, P., & Tenenbaum, J. B. (2017). Mind games: Game engines as an architecture for intuitive physics. Trends in Cognitive Sciences, 21(9), 649665.Google Scholar
Von Neumann, J., & Morgenstern, O. (1947). Theory of games and economic behavior. Princeton: Princeton University Press.Google Scholar
Voss, A., Nagler, M., & Lerche, V. (2013). Diffusion models in experimental psychology: A practical introduction. Experimental Psychology, 60(6), 385.Google Scholar
Vul, E., Frank, M. C., Tenenbaum, J. B., & Alvarez, G. A. (2009). Explaining human multiple object tracking as resource-constrained approximate inference in a dynamic probabilistic model. Advances in Neural Information Processing Systems, 22, 19551963.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, 599637.Google Scholar
Vul, E., & Pashler, H. (2008). Measuring the crowd within: Probabilistic representations within individuals. Psychological Science, 19, 645647.Google Scholar
Wald, A., & Wolfowitz, J. (1948). Optimum character of the sequential probability ratio test. Annals of Mathematical Statistics, 326–339.Google Scholar
Watkins, C. J., & Dayan, P. (1992). Q-learning: Machine learning, 8(3–4), 279292.Google Scholar
Williams, J. J., & Lombrozo, T. (2013). Explanation and prior knowledge interact to guide learning. Cognitive Psychology, 66(1), 5584.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org 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
×