Three case studies in the Bayesian analysis of cognitive models

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.

[1]  R. Shepard.  Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space , 1957 .

[2]  R. Shepard.  The analysis of proximities: Multidimensional scaling with an unknown distance function. II , 1962 .

[3]  R. Shepard.  The analysis of proximities: Multidimensional scaling with an unknown distance function. I. , 1962 .

[4]  J. Kruskal.  Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[5]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .

[6]  R. Rescorla,et al.  A theory of Pavlovian conditioning : Variations in the effectiveness of reinforcement and nonreinforcement , 1972 .

[7]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[8]  W. R. Garner.  The Processing of Information and Structure , 1974 .

[9]  R N Shepard,et al.  Multidimensional Scaling, Tree-Fitting, and Clustering , 1980, Science.

[10]  A. Tversky,et al.  Representations of qualitative and quantitative dimensions. , 1982, Journal of experimental psychology. Human perception and performance.

[11]  J. Ramsay.  Some Statistical Approaches to Multidimensional Scaling Data , 1982 .

[12]  R. Nosofsky.  American Psychological Association, Inc. Choice, Similarity, and the Context Theory of Classification , 2022 .

[13]  R. Nosofsky.  Attention, similarity, and the identification-categorization relationship. , 1986, Journal of experimental psychology. General.

[14]  R. Shepard,et al.  Toward a universal law of generalization for psychological science. , 1987, Science.

[15]  Neil A. Macmillan,et al.  Detection Theory: A User's Guide , 1991 .

[16]  John R. Anderson,et al.  The Adaptive Nature of Human Categorization , 1991 .

[17]  R. Shepard.  Integrality versus separability of stimulus dimensions: From an early convergence of evidence to a p , 1991 .

[18]  J. Kruschke,et al.  ALCOVE: an exemplar-based connectionist model of category learning. , 1992, Psychological review.

[19]  John K. Kruschke,et al.  Human Category Learning: Implications for Backpropagation Models , 1993 .

[20]  Gregory Ashby,et al.  On the Dangers of Averaging Across Subjects When Using Multidimensional Scaling or the Similarity-Choice Model , 1994 .

[21]  E. Wasserman,et al.  Cue Competition in Causality Judgments: The Role of Nonpresentation of Compound Stimulus Elements , 1994 .

[22]  P. Comon.  a Probabilistic Approach , 1995 .

[23]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[24]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[25]  G Gigerenzer,et al.  Reasoning the fast and frugal way: models of bounded rationality. , 1996, Psychological review.

[26]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[27]  I. J. Myung,et al.  Applying Occam’s razor in modeling cognition: A Bayesian approach , 1997 .

[28]  Peter Gr Unwald.  The minimum description length principle and reasoning under uncertainty , 1998 .

[29]  S. Sloman.  Categorical Inference Is Not a Tree: The Myth of Inheritance Hierarchies , 1998, Cognitive Psychology.

[30]  Jeffrey N. Rouder,et al.  Modeling Response Times for Two-Choice Decisions , 1998 .

[31]  Michael I. Jordan.  Graphical Models , 1998 .

[32]  Peter Grünwald.  Viewing all models as “probabilistic” , 1999, COLT '99.

[33]  Iver Mysterud,et al.  Take the best , 2000 .

[34]  E. Heit.  Properties of inductive reasoning , 2000, Psychonomic bulletin & review.

[35]  Peter Dayan,et al.  Explaining Away in Weight Space , 2000, NIPS.

[36]  I. J. Myung,et al.  GUEST EDITORS' INTRODUCTION: Special Issue on Model Selection , 2000 .

[37]  R. Shepard.  Perceptual-cognitive universals as reflections of the world. , 2001, The Behavioral and brain sciences.

[38]  M. Lee.  Determining the Dimensionality of Multidimensional Scaling Representations for Cognitive Modeling. , 2001, Journal of mathematical psychology.

[39]  J. Tenenbaum,et al.  Generalization, similarity, and Bayesian inference. , 2001, The Behavioral and brain sciences.

[40]  L. Rips.  Two Kinds of Reasoning , 2001 .

[41]  L M Parsons,et al.  New Evidence for Distinct Right and Left Brain Systems for Deductive versus Probabilistic Reasoning. , 2001, Cerebral cortex.

[42]  W. Michael Conklin,et al.  Monte Carlo Methods in Bayesian Computation , 2001, Technometrics.

[43]  I. J. Myung,et al.  Toward a method of selecting among computational models of cognition. , 2002, Psychological review.

[44]  M. Lee,et al.  Avoiding the dangers of averaging across subjects when using multidimensional scaling , 2003 .

[45]  M. Lee,et al.  Evidence accumulation in decision making: Unifying the “take the best” and the “rational” models , 2004, Psychonomic bulletin & review.

[46]  David Madigan,et al.  A Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets , 2003, Data Mining and Knowledge Discovery.

[47]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[48]  N. Brown,et al.  The role of guessing and boundaries on date estimation biases , 2004, Psychonomic bulletin & review.

[49]  Nick Chater,et al.  The Rational Analysis Of Mind And Behavior , 2000, Synthese.

[50]  J. Tenenbaum,et al.  Learning Domain Structures , 2004 .

[51]  Mark Steyvers,et al.  Finding scientific topics , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[52]  D. Medin,et al.  SUSTAIN: a network model of category learning. , 2004, Psychological review.

[53]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[54]  M. Lee,et al.  Common and distinctive features in stimulus similarity: A modified version of the contrast model , 2004, Psychonomic bulletin & review.

[55]  Joshua B. Tenenbaum,et al.  A Generative Theory of Similarity , 2005 .

[56]  Neil A. Macmillan,et al.  Detection theory: A user's guide, 2nd ed. , 2005 .

[57]  Evan Heit,et al.  Are There Two Kinds of Reasoning , 2005 .

[58]  J. Tenenbaum,et al.  Structure and strength in causal induction , 2005, Cognitive Psychology.

[59]  Jun Lu,et al.  An introduction to Bayesian hierarchical models with an application in the theory of signal detection , 2005, Psychonomic bulletin & review.

[60]  M. Lee,et al.  Bayesian statistical inference in psychology: comment on Trafimow (2003). , 2005, Psychological review.

[61]  Jeffrey N. Rouder,et al.  A hierarchical model for estimating response time distributions , 2005, Psychonomic bulletin & review.

[62]  Johanna D. Moore,et al.  Proceedings of the 28th Annual Conference of the Cognitive Science Society , 2005 .

[63]  M. Lee,et al.  Modeling individual differences in cognition , 2005, Psychonomic bulletin & review.

[64]  T. Griffiths,et al.  Modeling individual differences using Dirichlet processes , 2006 .

[65]  Michael D. Lee,et al.  A Hierarchical Bayesian Model of Human Decision-Making on an Optimal Stopping Problem , 2006, Cogn. Sci..

[66]  Thomas L. Griffiths,et al.  A more rational model of categorization , 2006 .

[67]  A. Yuille,et al.  Opinion TRENDS in Cognitive Sciences Vol.10 No.7 July 2006 Special Issue: Probabilistic models of cognition Vision as Bayesian inference: analysis by synthesis? , 2022 .

[68]  Thomas Hofmann,et al.  A Bayesian Approach to Diffusion Models of Decision-Making and Response Time , 2007 .

[69]  Charles Kemp,et al.  Bayesian models of cognition , 2008 .

[70]  Thomas L. Griffiths,et al.  A probabilistic approach to semantic representation , 2019, Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society.