A currently maturing line of work is attempting to apply Bayesian ideas in cognitive modeling, using the formalism provided by graphical modeling, and the sampling capabilities provided by WinBUGS. The idea is to tackle a broad range of models and see what Bayesian ideas can do for the models.

E.-J. Wagenmakers and I have a "work-in-progress" introduction to cognitive modeling using graphical models, coming from graduate teaching.

• The current 'coursebook' is here.
• The code for many of the chapters is here.

All of the code for the tutorials, and for the more specific projects below, relies on three bits of software.

• The first is Matlab.
• The second in WinBUGS, which can be downloaded and registered for free here.
• The third is Matbugs, which allows Matlab and WinBUGS to talk to each other, and can be downloaded for free here.

The following paper gives a set of graphical models for analyzing one limited form of multidimensional scaling (MDS), a version of Nosofsky's Generalized Context Model (GCM) of category learning, and a Signal Detection Theory (SDT) application to reasoning. The scripts that implement the graphical modeling part of the MDS and GCM examples are available here. The SDT example is essentially in the coursebook.

• Lee, M.D. (2008). Three case studies in the Bayesian analysis of cognitive models. Psychonomic Bulletin & Review, 15(1), 1-15. [pdf]

The following paper gives a very simple graphical model for the Bayesian inference of six equal-variance Gaussian Signal Detection Theory parameters. The software itself is available here, and the README for the software is here. At the encouragement of others, I wrote this paper as a sort of trojan horse to make a (relatively) broad audience aware of Bayesian graphical modeling, in a very familiar and simple context. This may or may not have been a good idea; there is no doubt the work of Jeff Rouder and colleagues is way ahead of this simple approach.

• Lee, M.D. (2008). BayesSDT: Software for Bayesian inference with signal detection theory. Behavior Research Methods, 40(2), 450-456. [pdf]

The following paper develops a graphical model for addressing some much-debated issues in the analysis of recognition memory. A demonstration of the software is available here.

• Dennis, S.J., Lee, M.D., & Kinnell, A. (2008). Bayesian analysis of recognition memory: The case of the list-length effect. Journal of Memory and Language, 59, 361-376. [pdf]

Finally, here are some other relevant papers, all using graphical modeling in the context of process models of cognition, and all (intended to be) tutorial-like in nature. 

• Shiffrin, R.M., Lee, M.D., Wagenmakers, E.-J., & Kim, W.J. (2008). A survey of model evaluation approaches with a focus on hierarchical Bayesian methods. Cognitive Science, 32(8), 1248-1284. [pdf]
• Lee, M.D., & Vanpaemel, W. (2008). Exemplars, prototypes, similarities and rules in category representation: An example of hierarchical Bayesian analysis. Cognitive Science, 32(8), 1403-1424. [pdf]
• Vandekerckhove, J., Tuerlinckx, F., & Lee, M.D. (submitted). Hierarchical diffusion models for two-choice response time.