Abstract
Bayesian statistical inference offers a principled and comprehensive approach for relating psychological models to data. This article presents Bayesian analyses of three influential psychological models: multidimensional scaling models of stimulus representation, the generalized context model of category learning, and a signal detection theory model of decision making. In each case, the model is recast as a probabilistic graphical model and is evaluated in relation to a previously considered data set. In each case, it is shown that Bayesian inference is able to provide answers to important theoretical and empirical questions easily and coherently. The generality of the Bayesian approach and its potential for the understanding of models and data in psychology are discussed.
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Anderson, J. R. (1991). The adaptive nature of human categorization. Psychological Review, 98, 409–429.
Ashby, F. G., Maddox, W. T., & Lee, W. W. (1994). On the dangers of averaging across subjects when using multidimensional scaling or the similarity-choice model. Psychological Science, 5, 144–151.
Chater, N., & Oaksford, M. (2000). The rational analysis of mind and behavior. Synthese, 122, 93–131.
Chen, M.-H., Shao, Q.-M., & Ibrahim, J. G. (2000). Monte Carlo methods in Bayesian computation. New York: Springer.
Dayan, P., & Kakade, S. (2001). Explaining away in weight space. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing systems 13 (pp. 451–457). Cambridge, MA: MIT Press.
Escobar, M. D., & West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, 577–588.
Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1, 209–230.
Garner, W. R. (1974). The processing of information and structure. Potomac, MD: Erlbaum.
Gati, I., & Tversky, A. (1982). Representations of qualitative and quantitative dimensions. Journal of Experimental Psychology: Human Perception & Performance, 8, 325–340.
Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1, 515–534.
Ghosh, J. K., & Ramamoorthi, R. V. (2003). Bayesian nonparametrics. New York: Springer.
Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103, 650–669.
Gilks, W. R., Richardson, S., & Spiegelhalter, D. J. (Eds.) (1996). Markov chain Monte Carlo in practice. Boca Raton, FL: Chapman & Hall/CRC.
Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. New York: Wiley.
Griffiths, T. L., Kemp, C., & Tenenbaum, J. B. (in press). Bayesian models of cognition. In R. Sun (Ed.), Cambridge handbook of computational cognitive modeling. Cambridge: Cambridge University Press.
Griffiths, T. L., & Steyvers, M. (2002). A probabilistic approach to semantic representation. In W. G. Gray & C. D. Schunn (Eds.), Proceedings of the 24th Annual Conference of the Cognitive Science Society (pp. 381–386). Mahwah, NJ: Erlbaum.
Griffiths, T. L., & Steyvers, M. (2004). Finding scientific topics. Proceedings of the National Academy of Sciences, 101, 5228–5235.
Griffiths, T. L., & Tenenbaum, J. B. (2005). Structure and strength in causal induction. Cognitive Psychology, 51, 354–384.
Grünwald, P. D. (1998). The minimum description length principle and reasoning under uncertainty. Amsterdam: University of Amsterdam, Institute for Logic, Language, and Computation.
Grünwald, P. D. (1999). Viewing all models as “probabilistic.” In S. Ben-David & P. Long (Eds.), Proceedings of the 12th Annual Conference on Computational Learning Theory (COLT ’99) (pp. 171–182). Santa Cruz, CA: ACM Press.
Heit, E. (2000). Properties of inductive reasoning. Psychonomic Bulletin & Review, 7, 569–592.
Heit, E., & Rotello, C. (2005). Are there two kinds of reasoning? In B. G. Bara, L. W. Barsalou, & M. Bucciarelli (Eds.), Proceedings of the 27th Annual Conference of the Cognitive Science Society (pp. 923–928). Mahwah, NJ: Erlbaum.
Helm, C. E. (1959). A multidimensional ratio scaling analysis of color relations. Princeton, NJ: Princeton University and Educational Testing Service.
Jordan, M. I. (2004). Graphical models. Statistical Science, 19, 140–155.
Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795.
Kemp, C., Bernstein, A., & Tenenbaum, J. B. (2005). A generative theory of similarity. In B. G. Bara, L. W. Barsalou, & M. Bucciarelli (Eds.), Proceedings of the 27th Annual Conference of the Cognitive Science Society (pp. 1132–1137). Mahwah, NJ: Erlbaum.
Kemp, C., Perfors, A., & Tenenbaum, J. B. (2004). Learning domain structures. In K. Forbus, D. Gentner, & T. Regier (Eds.), Proceedings of the 26th Annual Conference of the Cognitive Science Society (pp. 720–725). Mahwah, NJ: Erlbaum.
Kruschke, J. K. (1992). ALCOVE: An exemplar-based connectionist model of category learning. Psychological Review, 99, 22–44.
Kruschke, J. K. (1993). Human category learning: Implications for backpropagation models. Connection Science, 5, 3–36.
Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27.
Lee, M. D. (2001). Determining the dimensionality of multidimensional scaling representations for cognitive modeling. Journal of Mathematical Psychology, 45, 149–166.
Lee, M. D. (2006). A hierarchical Bayesian model of human decisionmaking on an optimal stopping problem. Cognitive Science, 30, 555–580.
Lee, M. D., & Cummins, T. D. R. v (2004). Evidence accumulation in decision making: Unifying the “take the best” and the “rational” models. Psychonomic Bulletin & Review, 11, 343–352.
Lee, M. D., Fuss, I. G., & Navarro, D. J. (2007). A Bayesian approach to diffusion models of decision-making and response time. In B. Schölkopf, J. C. Platt, & T. Hofmann (Eds.), Advances in neural information processing systems 19 (pp. 809–816). Cambridge, MA: MIT Press.
Lee, M. D., & Pope, K. J. (2003). Avoiding the dangers of averaging across subjects when using multidimensional scaling. Journal of Mathematical Psychology, 47, 32–46.
Lee, M. D., & Wagenmakers, E.-J. (2005). Bayesian statistical inference in psychology: Comment on Trafimow (2003). Psychological Review, 112, 662–668.
Lee, M. D., & Webb, M. R. (2005). Modeling individual differences in cognition. Psychonomic Bulletin & Review, 12, 605–621.
Love, B. C., Medin, D. L., & Gureckis, T. (2004). SUSTAIN: A network model of category learning. Psychological Review, 111, 309–332.
Mackay, D. J. C. (2003). Information theory, inference, and learning algorithms. Cambridge: Cambirdge University Press.
Macmillan, N. A., & Creelman, C. D. (2005). Detection theory: A user’s guide (2nd ed.). Mahwah, NJ: Erlbaum.
Myung, I. J., Forster, M., & Browne, M. W. (2000). A special issue on model selection. Journal of Mathematical Psychology, 44, 1–2.
Myung, I. J., & Pitt, M. A. (1997). Applying Occam’s razor in modeling cognition: A Bayesian approach. Psychonomic Bulletin & Review, 4, 79–95.
Navarro, D. J., Griffiths, T. L., Steyvers, M., & Lee, M. D. (2006). Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology, 50, 101–122.
Navarro, D. J., & Lee, M. D. (2004). Common and distinctive features in stimulus similarity: A modified version of the contrast model. Psychonomic Bulletin & Review, 11, 961–974.
Neal, R. M. (2000). Markov chain sampling methods for Dirichlet processes. Journal of Computational & Graphical Statistics, 9, 619–629.
Nosofsky, R. M. (1984). Choice, similarity, and the context theory of classification. Journal of Experimental Psychology: Learning, Memory, & Cognition, 10, 104–114.
Nosofsky, R. M. (1986). Attention, similarity, and the identification-categorization relationship. Journal of Experimental Psychology: General, 115, 39–57.
Parsons, L. M., & Osherson, D. (2001). New evidence for distinct right and left brain systems for deductive and probabilistic reasoning. Cerebral Cortex, 11, 954–965.
Pitt, M. A., Myung, I. J., & Zhang, S. (2002). Toward a method of selecting among computational models of cognition. Psychological Review, 109, 472–491.
Ramsay, J. O. (1982). Some statistical approaches to multidimensional scaling data. Journal of the Royal Statistical Society A, 145, 285–312.
Rescorla, R. A., & Wagner, A. R. (1972). A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. In A. H. Black & W. F. Prokasy (Eds.), Classical conditioning II: Current research and theory (pp. 64–99). New York: Appleton-Century-Crofts.
Ridgeway, G., & Madigan, D. (2003). A sequential Monte Carlo method for Bayesian analysis of massive datasets. Data Mining & Knowledge Discovery, 7, 301–319.
Rips, L. J. (2001). Two kinds of reasoning. Psychological Science, 12, 129–134.
Rouder, J. N., & Lu, J. (2005). An introduction to Bayesian hierarchical models with an application in the theory of signal detection. Psychonomic Bulletin & Review, 12, 573–604.
Rouder, J. N., Lu, J., Speckman, P., Sun, D., & Jiang, Y. (2005). A hierarchical model for estimating response time distributions. Psychonomic Bulletin & Review, 12, 195–223.
Sanborn, A. N., Griffiths, T. L., & Navarro, D. J. (2006). A more rational model of categorization. In R. Sun & N. Miyake (Eds.), Proceedings of the 28th Annual Conference of the Cognitive Science Society (pp. 726–731). Mahwah, NJ: Erlbaum.
Shepard, R. N. (1957). Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 22, 325–345.
Shepard, R. N. (1962). The analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika, 27, 125–140.
Shepard, R. N. (1980). Multidimensional scaling, tree-fitting, and clustering. Science, 210, 390–398.
Shepard, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237, 1317–1323.
Shepard, R. N. (1991). Integrality versus separability of stimulus dimensions: From an early convergence of evidence to a proposed theoretical basis. In J. R. Pomerantz & G. L. Lockhead (Eds.), The perception of structure: Essays in honor of Wendell R. Garner (pp. 53–71). Washington, DC: American Psychological Association.
Shepard, R. N. (1994). Perceptual-cognitive universals as reflections of the world. Psychonomic Bulletin & Review, 1, 2–28.
Sloman, S. A. (1998). Categorical inference is not a tree: The myth of inheritance hierarchies. Cognitive Psychology, 35, 1–33.
Spiegelhalter, D. J., Thomas, A., & Best, N. G. (2004). WinBUGS Version 1.4 user manual. Cambridge: Medical Research Council Biostatistics Unit.
Spiegelhalter, D. J., Thomas, A., Best, N. G., & Gilks, W. R. (1996). BUGS Examples Volume 1, Version 0.5. Cambridge: Medical Research Council Biostatistics Unit.
Tenenbaum, J. B., & Griffiths, T. L. (2001). Generalization, similarity, and Bayesian inference. Behavioral & Brain Sciences, 24, 629–640.
Treat, T. A., MacKay, D. B., & Nosofsky, R. M. (1999, July). Probabilistic scaling: Basic research and clinical applications. Paper presented at the 32nd Annual Meeting of the Society for Mathematical Psychology, Santa Cruz, CA.
Van Hamme, L. J., & Wasserman, E. A. (1994). Cue competition in causality judgments: The role of nonrepresentation of compound stimulus elements. Learning & Motivation, 25, 127–151.
Yuille, A. L., & Kersten, D. (2006). Vision as Bayesian inference: Analysis by synthesis? Trends in Cognitive Sciences, 10, 301–308.
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Lee, M.D. Three case studies in the Bayesian analysis of cognitive models. Psychonomic Bulletin & Review 15, 1–15 (2008). https://doi.org/10.3758/PBR.15.1.1
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DOI: https://doi.org/10.3758/PBR.15.1.1