Lewandowsky, S, Farrel, S. Computational Modeling in Cognition: Principles and Practice. Thousand Oaks, CA: Sage Publications; 2011.

Ratcliff, R, Smith, PL. A comparison of sequential sampling models for two‐choice reaction time. Psychol Rev 2004, 111:333–367.

Nosofsky, RM. %22Exemplar‐based approach to relating categorization, identification, and recognition%22. In: Ashby, G, ed. Multidimensional Models of Perception and Cognition. Hillsdale, NJ: Lawrence Erlbaum; 1992, 363–394.

Richler, JJ, Palmeri, TJ. Visual category learning. WIREs Cogn Sci 2014, 5:75–94.

Polyn, SM, Norman, KA, Kahana, MJ. A context maintenance and retrieval model of organizational processes in free recall. Psychol Rev 2009, 116:129–156.

Turner, BM, Forstmann, BU, Love, BC, Palmeri, TJ. Approaches to analysis in model‐based cognitive neuroscience. J Math Psychol 2017, 76:65–79. https://doi.org/10.1016/j.jmp.2016.01.001.

Bartlema, A, Lee, MD, Wetzels, R, Vanpaemel, W. A Bayesian hierarchical mixture approach to individual differences: case studies in selective attention and representation in category learning. J Math Psychol 2014, 59:132–150.

Shen, J, Palmeri, T. Modelling individual difference in visual categorization. Vis Cogn 2016, 24:260–283. https://doi.org/10.1080/13506285.2016.1236053.

Wiecki, TV, Poland, J, Frank, MJ. Model‐based cognitive neuroscience approaches to computational psychiatry: Clustering and classification. Clin Psychol Sci 2015, 3:378–399.

Myung, IJ, Pitt, MA. Applying Occam`s razor in modeling cognition: a Bayesian approach. Psychon Bull Rev 1997, 4:79–95.

Busemeyer, JR, Diederich, A. Cognitive Modeling. Thousand Oaks, CA: Sage Publications; 2010.

Newell, A. You Can`t Play 20 Questions with Nature and Win : Projective Comments on the Papers of this Symposium. New York: Academic Press; 1973.

Allport, DA. Critical notice: The state of cognitive psychology. Q J Exp Psychol 1975, 27:141–152.

Shiffrin, RM, Nobel, PA. The art of model development and testing. Behav Res Methods Instrum Comput 1997, 29:6–14.

Polk, TA, Seifert, CM. Cognitive Modeling. Cambridge, MA: MIT Press; 2002.

Clark, SE, Gronlund, SD. Global matching models of recognition memory: how the models match the data. Psychon Bull Rev 1996, 3:37–60. https://doi.org/10.3758/BF03210740.

Pothos, EM, Wills, AJ. Formal Approaches to Categorization. Cambridge, UK: Cambridge University Press; 2011.

Palmeri, TJ, Love, BC, Turner, BM. Model‐based cognitive neuroscience. J Math Psychol. 2017, 76:59–64. https://doi.org/10.1016/j.jmp.2016.10.010.

Jacobs, RA, Kruschke, JK. Bayesian learning theory applied to human cognition. WIREs Cogn Sci 2011, 2:8–21.

Griffiths, T, Kemp, C, Tenenbaum, J. %22Bayesian models of cognition%22. In: Sun, R, ed. The Cambridge Handbook of Expertise and Expert Performance. New York: Cambridge University Press; 2008, 59–100.

Anderson, JR. The Adaptive Character of Thought. Hillsdale NJ: Lawrence Erlbaum; 1990.

Jones, M, Love, BC. Bayesian fundamentalism or enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition. Behav Brain Sci 2011, 34:169–231.

Kruschke, JK. Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan. 2nd ed. Burlington, MA: Academic Press; 2014.

Jackman, S. Bayesian Analysis for the Social Sciences. Hoboken, NJ: John Wiley %26 Sons; 2009.

Gelman, A, Carlin, JB, Stern, HS, Rubin, DB. Bayesian Data Analysis. Boca Raton, FL: Chapman %26 Hall/CRC; 2014.

Myung, IJ. Tutorial on maximum likelihood estimation. J Math Psychol 2003, 47:90–100.

Carpenter, B, Gelman, A, Hoffman, M, Lee, D, Goodrich, B, Betancourt, M, et al. Stan: a probabilistic programming language. J Stat Softw 2016, 76:1–32.

Nelder, JA, Mead, R. A simplex method for function minimization. Comput J 1964, 7:308–313. https://doi.org/10.1093/comjnl/7.4.308.

Wagenmakers, E‐J, Ratcliff, R, Gomez, R, Iverson, GJ. Assessing model mimicry using the parametric bootstrap. J Math Psychol. 2004, 48:28–50.

Schwarz, G. Estimating the dimension of a model. Ann Stat 1978, 6:461–464. https://doi.org/10.1214/aos/1176344136.

Akaike, H. A new look at the statistical model identification. IEEE Trans Autom Control 1974, 19:716–723. https://doi.org/10.1109/TAC.1974.1100705.

Chater, N, Oaksford, M, Hahn, U, Heit, E. Bayesian models of cognition. WIREs Cogn Sci. 2010, 1:811–823.

Kruschke, JK. Bayesian data analysis. WIREs Cogn Sci 2010, 1:658–676.

Bernardo, JM, Smith, AFM. Bayesian Theory. New York: Wiley; 1994.

de Finetti, B. %22Foresight: its logical laws in subjective sources%22. In: Kyburg, H, Smokler, H, eds. Studies in Subjective Probability. New York: Wiley; 1964, 93–158.

Bayes, T. A letter from the late reverend Mr. Thomas Bayes, FRS to John Canton, MA and FRS. Philos Trans 1763, 53:269–271.

Lee, MD. Three case studies in the Bayesian analysis of cognitive models. Psychon Bull Rev 2008, 15:1–15.

Rouder, JN, Lu, J. An introduction to Bayesian hierarchical models with an application in the theory of signal detection. Psychon Bull Rev 2005, 12:573–604.

Matzke, D, Dolan, CV, Batchelder, WH, Wagenmakers, E‐J. Bayesian estimation of multinomial processing tree models with heterogeneity in participants and items. Psychometrika 2015, 80:205–235.

Katahira, K. How hierarchical models improve point estimates of model parameters at the individual level. J Math Psychol 2016, 73:37–58. https://doi.org/10.1016/j.jmp.2016.03.007.

Lee, MD, Webb, MR. Modeling individual differences in cognition. Psychon Bull Rev 2005, 12:605–621.

Okada, K, Lee, MD. A Bayesian approach to modeling group and individual differences in multidimensional scaling. J Math Psychol 2016, 70:35–44.

Merkle, EC, Smithson, M, Verkuilen, J. Hierarchical models of simple mechanisms underlying confidence in decision making. J Math Psychol 2011, 55:57–67 https://doi.org/10.1016/j.jmp.2010.08.011.

Ravenzwaaij, D, Moore, CP, Lee, MD, Newell, BR. A hierarchical Bayesian modeling approach to searching and stopping in multi‐attribute judgment. Cogn Sci 2014, 38:1384–1405.

Annis, J, Miller, BJ, Palmeri, TJ. Bayesian inference with Stan: a tutorial on adding custom distributions. Behav Res Methods 2016, 49:863–886.

Ratcliff, R, Childers, R. Individual differences and fitting methods for the two‐choice diffusion model of decision making. Decision 2015, 2:237–279.

Vandekerckhove, J, Tuerlinckx, F, Lee, MD. Hierarchical diffusion models for two‐choice response times. Psychol Methods 2011, 16:44–62.

Wiecki, TV, Sofer, I, Frank, MJ. HDDM: hierarchical bayesian estimation of the drift‐diffusion model in python. Front Neuroinform 2013, 7:14.

Annis, J, Lenes, JG, Westfall, HA, Criss, AH, Malmberg, KJ. The list‐length effect does not discriminate between models of recognition memory. J Mem Lang 2015, 85:27–41.

Dennis, S, Lee, MD, Kinnell, A. Bayesian analysis of recognition memory: the case of the list‐length effect. J Mem Lang 2008, 59:361–376.

Morey, RD. A Bayesian hierarchical model for the measurement of working memory capacity. J Math Psychol 2011, 55:8–24. https://doi.org/10.1016/j.jmp.2010.08.008.

Pratte, MS, Rouder, JN. Hierarchical single‐ and dual‐process models of recognition memory. J Math Psychol 2011, 55:36–46. https://doi.org/10.1016/j.jmp.2010.08.007.

Turner, BM, Forstmann, BU, Wagenmakers, E‐J, Brown, SD, Sederberg, PB, Steyvers, M. A Bayesian framework for simultaneously modeling neural and behavioral data. Neuroimage 2013, 72:193–206. https://doi.org/10.1016/j.neuroimage.2013.01.048.

Brown, SD, Heathcote, A. The simplest complete model of choice response time: linear ballistic accumulation. Cogn Psychol 2008, 57:153–178.

Lee, MD, Wagenmakers, E‐J. Bayesian Cognitive Modeling: A Practical Course. Cambridge, UK: Cambridge University Press; 2014.

Lee, MD. How cognitive modeling can benefit from hierarchical Bayesian models. J Math Psychol 2011, 55:1–7.

Shiffrin, RM, Lee, MD, Kim, W, Wagenmakers, E‐J. A survey of model evaluation approaches with a tutorial on hierarchical bayesian methods. Cogn Sci 2008, 32:1248–1284.

Lynch, SM. Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. New York: Springer Science %26 Business Media; 2007.

Usher, M, McClelland, JL. The time course of perceptual choice: the leaky, competing accumulator model. Psychol Rev 2001, 108:550–592.

Hyndman, RJ. Computing and graphing highest density regions. Am Stat 1996, 50:120–126.

Jaynes, ET, Kempthorne, O. %22Confidence intervals vs Bayesian intervals%22. In: Harper, WL, Hooker, C, eds. Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Dordrecht, The Netherlands: Springer; 1976, 175–257.

Morey, RD, Hoekstra, R, Rouder, JN, Lee, MD, Wagenmakers, E‐J. The fallacy of placing confidence in confidence intervals. Psychon Bull Rev 2016, 23:103–123. https://doi.org/10.3758/s13423-015-0947-8.

Lindley, D. That wretched prior. Significance 2004, 1:85–87.

Efron, B. Why isn`t everyone a Bayesian? Am Stat. 1986, 40:1–5.

Lee, MD, Vanpaemel, W. Determining informative priors for cognitive models. Psychon Bull Rev 2017. https://doi.org/10.3758/s13423‐017‐1238‐3.

Vanpaemel, W, Lee, MD. Using priors to formalize theory: optimal attention and the generalized context model. Psychon Bull Rev 2012, 19:1047–1056. https://doi.org/10.3758/s13423-012-0300-4.

Jeffreys, H. Theory of Probability. 3rd ed. Oxford, UK: Oxford University Press; 1961.

Kass, RE, Wasserman, L. The selection of prior distributions by formal rules. J Am Stat Assoc 1996, 91:1343–1370.

Spiegelhalter, DJ, Smith, AFM. Exact and approximate posterior moments for a normal location. J R Stat Soc Ser B Stat Methodol. 1982, 54:793–804.

Brooks, S, Gelman, A, Jones, G, Meng, X‐L. Handbook of Markov Chain Monte Carlo. Boca Raton, FL: Chapman %26 Hall/CRC Press; 2011.

Green, PJ, Łatuszyński, K, Pereyra, M, Robert, CP. Bayesian computation: a summary of the current state, and samples backwards and forwards. Stat Comput 2015, 25:835–862.

van Ravenzwaaij, D, Cassey, P, Brown, SD. A simple introduction to Markov chain Monte Carlo sampling. Psychon Bull Rev 2016. https://doi.org/10.3758/s13423-016-1015-8.

Metropolis, N, Rosenbluth, AW, Rosenbluth, MN, Teller, AH, Teller, E. Equation of state calculations by fast computing machines. J Chem Phys 1953, 21:1087–1092. https://doi.org/10.1063/1.1699114.

Hastings, WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 1970, 57:97–109.

Gelfand, A, Smith, A. Sampling‐based approaches to calculating marginal densities. J Am Stat Assoc 1990, 85:398–409.

Geman, S, Geman, D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 1984, PAMI‐6:721–741.

Gilks, WR, Best, NG, Tan, KKC. Adaptive rejection metropolis sampling within Gibbs sampling. J R Stat Soc Ser C Appl Stat 1995, 44:455–472.

Lunn, DJ, Thomas, A, Best, N, Spiegelhalter, D. WinBUGS – a Bayesian modelling framework: concepts, structure, and extensibility. Stat Comput. 2000, 10:325–337.

Plummer, M. JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In: *Proceedings of 3rd International Workshop on Distributed Statistical Computing* (DSC 2003), 2003, 20–2. doi:https://doi.org/10.1.1.13.3406.

Neal, RM. %22MCMC using Hamiltonian dynamics%22. In: Brooks, S, Gelman, A, Jones, G, Meng, X‐L, eds. Handbook of Markov Chain Monte Carlo. Boca Raton, FL: Chapman %26 Hall/CRC Press; 2011, 113–162.

Wabersich, D, Vandekerckhove, J, Extending, JAGS. A tutorial on adding custom distributions to JAGS (with a diffusion model example). Behav Res Methods 2014, 46:15–28. https://doi.org/10.3758/s13428-013-0369-3.

Donkin, C, Brown, S, Heathcote, A. Drawing conclusions from choice response time models: a tutorial using the linear ballistic accumulator. J Math Psychol 2011, 55:140–151.

Holmes, WR. A practical guide to the probability density approximation (PDA) with improved implementation and error characterization. J Math Psychol 2015, 68–69:13–24.

Turner, BM, Sederberg, PB. Approximate Bayesian computation with differential evolution. J Math Psychol 2012, 56:375–385. https://doi.org/10.1016/j.jmp.2012.06.004.

Turner, BM, Sederberg, PB, McClelland, JL. Bayesian analysis of simulation‐based models. J Math Psychol 2014, 72:191–199. https://doi.org/10.1016/j.jmp.2014.10.001.

Turner, BM, Van Zandt, T. A tutorial on approximate Bayesian computation. J Math Psychol 2012, 56:69–85. https://doi.org/10.1016/j.jmp.2012.02.005.

Turner, BM, Van Zandt, T. Hierarchical approximate Bayesian computation. Psychometrika 2013, 79:185–209.

Gelman, A. Two simple examples for understanding posterior p‐values whose distributions are far from uniform. Electron J Stat 2013, 7:2595–2602.

Zhang, JL. Comparative investigation of three Bayesian p values. Comput Stat Data Anal 2014, 79:277–291. https://doi.org/10.1016/j.csda.2014.05.012.

Kruschke, JK. Posterior predictive checks can and should be Bayesian: comment on Gelman and Shalizi, “philosophy and the practice of Bayesian statistics”. Br J Math Stat Psychol 2013, 66:45–56.

Myung, IJ. The importance of complexity in model selection. J Math Psychol 2000, 44:190–204. https://doi.org/10.1006/jmps.1999.1283.

Good, IJ. The interface between statistics and philosophy of science. Stat Sci 1988, 3:386–412. https://doi.org/10.1214/ss/1177013604.

Kass, RE, Raftery, AE. Bayes factors. J Am Stat Assoc 1995, 90:773–795.

Shiffrin, RM, Chandramouli, SH, Grunwald, PD. Bayes factors, relations to minimum description length, and overlapping model classes. J Math Psychol. 2015, 72:56–77. https://doi.org/10.1016/j.jmp.2015.11.002.

Kruschke, JK. Bayesian assessment of values via parameter estimation and model comparison. Perspect Psychol Sci 2011, 6:299–312.

Liu, CC, Aitkin, M. Bayes factors: prior sensitivity and model generalizability. J Math Psychol 2008, 52:362–375. https://doi.org/10.1016/j.jmp.2008.03.002.

Vanpaemel, W. Prior sensitivity in theory testing: an apologia for the Bayes factor. J Math Psychol 2010, 54:491–498. https://doi.org/10.1016/j.jmp.2010.07.003.

Evans, NJ, Brown, SD. Bayes factors for the Linear Ballistic Accumulator Model of Decision‐Making. Behav Res Methods 2017. https://doi.org/10.3758/s13428-017-0887-5.

Luebke, D. CUDA: Scalable parallel programming for high‐performance scientific computing. In: *5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008 ISBI 2008*, 2008, 836–838.

Wagenmakers, E‐J, Lodewyckx, T, Kuriyal, H, Grasman, R. Bayesian hypothesis testing for psychologists: a tutorial on the savage‐dickey method. Cogn Psychol 2010, 60:158–189. https://doi.org/10.1016/j.cogpsych.2009.12.001.

Morey, RD, Rouder, JN, Pratte, MS, Speckman, PL. Using MCMC chain outputs to efficiently estimate Bayes factors. J Math Psychol 2011, 55:368–378.

Friel, N, Wyse, J. Estimating the evidence ‐ a review. Stat Neerl 2012, 66:288–308.

Geweke, BYJ. Bayesian inference in iconometric models using monte carlo integration. Econometrica 1989, 57:1317–1339.

Newton, M, Raftery, A. Approximate Bayesian inference with the weighted likelihood bootstrap. J R Stat Soc Ser B Stat Methodol 1994, 56:3–48.

Neal, RM. Annealed importance sampling. Stat Comput 2001, 11:125–139.

Meng, X‐L, Wong, HW. Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Stat Sin 1996, 6:831–860.

Chib, S, Jeliazkov, I. Marginal likelihood from the metropolis‐Hastings output. J Am Stat Assoc 2001, 96:270–281 https://doi.org/10.2307/2291521.

Chib, S. Marginal likelihood from the Gibbs output. J Am Stat Assoc 1995, 90:1313–1321. https://doi.org/10.2307/2291521.

Skilling, J. Nested sampling for Bayesian computations. Bayesian Anal 2006, 1:833–860. https://doi.org/10.1214/06-BA127.

Friel, N, Pettitt, AN. Marginal likelihood estimation via power posteriors. J R Stat Soc Ser B Stat Methodol. 2008, 70:589–607.

Lartillot, N, Philippe, H. Computing bayes factors using thermodynamic integration. Syst Biol 2006, 55:195–207. https://doi.org/10.1080/10635150500433722.

Liu, P, Elshall, AS, Ye, M, Beerli, P, Zeng, X, Lu, D, Tao, Y. Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods. Water Resour Res 2016, 52:734–758.

Green, PJ. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 1995, 82:711–732.

Carlin, BP, Chib, S. Bayesian model choice via Markov chain Monte Carlo methods. J R Stat Soc Ser B (Stat Methodol) 1995, 57:473–484.

Lodewyckx, T, Kim, W, Lee, MD, Tuerlinckx, F, Kuppens, P, Wagenmakers, E‐J. A tutorial on Bayes factor estimation with the product space method. J Math Psychol. 2011, 55:331–347.

Ando, T. Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models. Biometrika 2017, 94:443–458.

Friel, N, Mckeone, JP, Oates, CJ, Pettitt, AN. Investigation of the widely applicable Bayesian information criterion. Stat Comput 2016, 27:833–844.

Watanabe, S. A widely applicable Bayesian information criterion. Mach Learn Res 2013, 14:867–897.

Gelman, A, Hwang, J, Vehtari, A. Understanding predictive information criteria for Bayesian models. Stat Comput 2014, 24:997–1016.

Watanabe, S. Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res 2010, 11:3571–3594.

Spiegelhalter, DJ, Best, NG, Carlin, BP, van der Linde, A. Bayesian measures of model complexity and fit. J R Stat Soc Ser B Stat Methodol 2002, 64:583–639.

Lee, MD, Wagenmakers, E‐J. Bayesian statistical inference in psychology: comment on Trafimow (2003). Psychol Rev. 2005, 112:662–668.

Lee, MD. Determining the dimensionality of multidimensional scaling representations for cognitive modeling. J Math Psychol 2001, 45:149–166. https://doi.org/10.1006/jmps.1999.1300.

Rouder, JN, Lu, J, Speckman, P, Sun, D. A hierarchical model for estimating response time distributions. Psychon Bull Rev 2005, 12:195–223.

Vanpaemel, W. Constructing informative model priors using hierarchical methods. J Math Psychol 2011, 55:106–117. https://doi.org/10.1016/j.jmp.2010.08.005.

Nosofsky, RM. Attention, similarity, and the identification‐categorization relationship. J Exp Psychol Gen 1986, 115:39–57.

Sinharay, S, Stern, HS. On the sensitivity of Bayes factors to the prior distributions. Am Stat 2002, 56:196–201.

Rouder, JN, Morey, RD, Pratte, MS. %22Hierarchical Bayesian models%22. In: Batchelder, WH, Colonius, H, Dzhafarov, E, Myung, JI, eds. New Handbook of Mathematical Psychology. Measurement and Methodology, vol. 1. London, UK: Cambridge University Press; 2013.

Estes, WK. The problem of inference from curves based on group data. Psychol Bull 1956, 53:134–140.

Cohen, AL, Sanborn, AN, Shiffrin, RM. Model evaluation using grouped or individual data. Psychon Bull Rev 2008, 15:692–712.

Ashby, FG, Maddox, WT, Lee, WW. On the dangers of averaging across subjects when using multidimensional scaling or the similarity choice model. Psychol Sci 1994, 5:144–151.

Lee, MD, Pope, KJ. Avoiding the dangers of averaging across subjects when using multidimensional scaling. J Math Psychol. 2003, 47:32–46.