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Chapter 22 - Sampling Data, Beliefs, and Actions

from Part VI - Computational Approaches

Published online by Cambridge University Press:  01 June 2023

By
Erik Brockbank ,
Cameron Holdaway ,
Daniel Acosta-Kane  and
Edward Vul
Edited by
Klaus Fiedler ,
Peter Juslin  and
Jerker Denrell
Klaus Fiedler
Affiliation:
Universität Heidelberg
Peter Juslin
Affiliation:
Uppsala Universitet, Sweden
Jerker Denrell
Affiliation:
University of Warwick
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Summary

Sampling – using a stochastically drawn subset of possibilities – has been at the core of many influential modeling frameworks of human decision making for the last half century. Although these frameworks all refer to their core operation as “sampling,” they differ dramatically in the behaviors and inferences they aim to account for. Here we review this landscape of sampling models under a unified expected utility framework which treats diverse sampling accounts as approximating different terms in the expected utility calculation. We show that a broad range of sample-based models in psychology are built around sampled data, beliefs, or actions and can therefore support downstream expected utility maximization. To compare these models on an even footing, our review focuses on how the number of samples and the sample distribution differ within each element of the expected utility calculation. This integrated summary allows us to identify opportunities for fruitful cross-pollination across sampling domains, and to highlight outstanding challenges for accounts that might aim to integrate these disparate models.

Keywords

samplingdatabeliefsactionsexpected utility
Type
Chapter
Information
Sampling in Judgment and Decision Making , pp. 513 - 548
Publisher: Cambridge University Press
Print publication year: 2023

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References

Adams, G. S., Converse, B. A., Hales, A. H., & Klotz, L. E. (2021). People systematically overlook subtractive changes. Nature, 592(7853), 258–261.Google Scholar
Baker, C. L., Saxe, R., & Tenenbaum, J. B. (2009). Action understanding as inverse planning. Cognition, 113(3), 329–349.CrossRefGoogle ScholarPubMed
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), 18327–18332.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, 35–65.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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), 519–527.CrossRefGoogle ScholarPubMed
Chater, N., Tenenbaum, J. B., & Yuille, A. (2006). Probabilistic models of cognition: Where next? Trends in Cognitive Sciences, 10(7), 292–293.Google Scholar
Chernev, A., Böckenholt, U., & Goodman, J. (2015). Choice overload: A conceptual review and meta-analysis. Journal of Consumer Psychology, 25(2), 333–358.Google Scholar
Coenen, A., & Gureckis, T. (2021). The distorting effects of deciding to stop sampling information. PsyArXiv. doi:10.31234/osf.io/tbreaCrossRefGoogle Scholar
Dasgupta, I., & Gershman, S. J. (2021). Memory as a computational resource. Trends in Cognitive Sciences, 25(3), 240–251.Google Scholar
Dasgupta, I., Schulz, E., & Gershman, S. J. (2017). Where do hypotheses come from? Cognitive Psychology, 96, 1–25.Google Scholar
Dasgupta, I., Schulz, E., Goodman, N. D., & Gershman, S. J. (2018). Remembrance of inferences past: Amortization in human hypothesis generation. Cognition, 178, 67–81.Google Scholar
Dasgupta, I., Schulz, E., Tenenbaum, J. B., & Gershman, S. J. (2020). A theory of learning to infer. Psychological Review, 127(3), 412.CrossRefGoogle ScholarPubMed
Daw, N., & Courville, A. (2008). The pigeon as particle filter. Advances in Neural Information Processing Systems, 20, 369–376.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), 876–879.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), 285–300.CrossRefGoogle ScholarPubMed
Doucet, A., de Freitas, N., & Gordon, N. (Eds.) (2001). Sequential Monte Carlo methods in practice. New York: Springer.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Fiedler, K. (2008). The ultimate sampling dilemma in experience-based decision making. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34(1), 186.Google ScholarPubMed
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. 3–32). 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), 1515–1523.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), 273–278.CrossRefGoogle ScholarPubMed
Gershman, S. J., Vul, E., & Tenenbaum, J. B. (2012). Multistability and perceptual inference. Neural Computation, 24(1), 1–24.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.CrossRefGoogle Scholar
Gilks, W. R., Richardson, S., & Spiegelhalter, D. (1995). Markov chain Monte Carlo in practice. Boca Raton, FL: CRC Press.Google Scholar
Gittins, J. C. (1979). Bandit processes and dynamic allocation indices. Journal of the Royal Statistical Society: Series B (Methodological), 41(2), 148–164.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), 585–595.CrossRefGoogle ScholarPubMed
Goodman, N. D., Tenenbaum, J. B., Feldman, J., & Griffiths, T. L. (2008). A rational analysis of rule-based concept learning. Cognitive Science, 32(1), 108–154.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), 87–92.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), 7892–7899.CrossRefGoogle ScholarPubMed
Griffiths, T. L., & Tenenbaum, J. B. (2006). Optimal predictions in everyday cognition. Psychological Science, 17(9), 767–773.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), 263–268.CrossRefGoogle 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), 48–68.Google Scholar
Hauser, J. R., & Wernerfelt, B. (1990). An evaluation cost model of consideration sets. Journal of Consumer Research, 16(4), 393–408.Google Scholar
Hayden, B., & Niv, Y. (2020). The case against economic values in the brain. Behavioral Neuroscience, 135(2), 192–201.CrossRefGoogle 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, 534–539.CrossRefGoogle ScholarPubMed
Hertwig, R., & Erev, I. (2009). The description–experience gap in risky choice. Trends in Cognitive Sciences, 13, 517–523.CrossRefGoogle ScholarPubMed
Hertwig, R., & Pleskac, T. J. (2010). Decisions from experience: Why small samples? Cognition, 115, 225–237.CrossRefGoogle ScholarPubMed
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), 379–385.CrossRefGoogle 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), 912–915.Google Scholar
Johnson, J. G., & Raab, M. (2003). Take the first: Option-generation and resulting choices. Organizational Behavior and Human Decision Processes, 91(2), 215–229.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.CrossRefGoogle ScholarPubMed
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–292.CrossRefGoogle 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), 814–829.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), 111–121.Google Scholar
Klayman, J., & Ha, Y.-W. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94(2), 211.CrossRefGoogle 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), 779–784.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, 937–944.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), 969–998.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), 322–349.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), 805–824.Google Scholar
Loomes, G., & Sugden, R. (1986). Disappointment and dynamic consistency in choice under uncertainty. Review of Economic Studies, 53(2), 271–282.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), 284–299.CrossRefGoogle ScholarPubMed
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), 423–429.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), 1731–1746.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), 1133–1147.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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, 1026–1040.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), 873–922.CrossRefGoogle ScholarPubMed
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, 69–89.Google Scholar
Sanborn, A. N. (2017). Types of approximation for probabilistic cognition: Sampling and variational. Brain and Cognition, 112, 98–101.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), 1561–1572.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), 443–464.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), 64–75.Google Scholar
Stewart, N., Chater, N., & Brown, G. D. (2006). Decision by sampling. Cognitive Psychology, 53, 1–26.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), 1279–1285.CrossRefGoogle 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), 285–294.CrossRefGoogle Scholar
Tversky, A., & Kahneman, D. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291.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), 649–665.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, 1955–1963.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, 599–637.Google Scholar
Vul, E., & Pashler, H. (2008). Measuring the crowd within: Probabilistic representations within individuals. Psychological Science, 19, 645–647.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), 279–292.Google Scholar
Williams, J. J., & Lombrozo, T. (2013). Explanation and prior knowledge interact to guide learning. Cognitive Psychology, 66(1), 55–84.Google Scholar

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