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On Cross Validated there is a great question about best introductory books for bayesian statistics. Also, Jeromy Anglim blogged recently about use of JAGS, rjags, and Bayesian Modelling, with some very nice collection of tutorials relevant to the above question. Lots of those resources are single-shot tutorials, covering just some limited scope of programming and modelling.

In terms of resources that cover a broader range of topics with some background information and coding tutorials, only two sources stand out from the list:

Those two books could potentially hit the spot in terms of sufficient coverage of basic needs for beginner bayesian acolyte.

What else do you advise as a simple, practical, compact, and thorough introduction to bayesian modeling for a cognitive scientist?

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+1 to Speldosa's suggestion. Griffiths and colleagues have written several primers on the use of Bayesian models in cogsci. Many of them can be found on Griffiths' website under 'Foundations':

http://cocosci.berkeley.edu/publications.php?topic=Foundations

e.g.

Perfors, A., Tenenbaum, J.B., Griffiths, T. L., & Xu, F. (2011). A tutorial introduction to Bayesian models of cognitive development. Cognition, 120, 302-321.

Griffiths, T. L., & Yuille, A. (2008). A primer on probabilistic inference. In M. Oaksford and N. Chater (Eds.). The probabilistic mind: Prospects for rational models of cognition. Oxford: Oxford University Press.

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Reading list

As @Jeff has mentioned Tom Griffiths has several useful resources. In particular Tom Griffiths has an extensive reading list that you might find relevant. To quote the summary of the content:

This list is intended to introduce some of the tools of Bayesian statistics and machine learning that can be useful to computational research in cognitive science. The first section mentions several useful general references, and the others provide supplementary readings on specific topics...

Other comments

  • More broadly, it certainly helps when learning Bayesian statistics to have a good understanding of calculus (integration is key) and probability (distributions, how they are parameterised, etc.).
  • John Kruschke's book is quite accessible
  • Gelman and Hill is also quite accessible; the focus is multilevel modelling and regression; it covers Bayesian modelling with BUGS. It is very readable and has lots of practical advice. That said, it's doesn't specifically address issues related to cognitive science.
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    $\begingroup$ Thanks - great list of resources on your blog by the way! I would also add matrix algebra to pre-requirements for learning Bayesian stats. Regarding "basic mathematics", this book by Scott Lynch is also nice introductory source. In the appendix there is a compact overview of calculus and matrix algebra - a nice addition that many books on the topic lacks. $\endgroup$
    – Geek On Acid
    Apr 19, 2012 at 13:55
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In the fairly recent book "The Cambridge Handbook of Computational Psychology", chapter three is devoted to bayesian modeling. It's written by Thomas Griffiths, Charles Kemp, and Joshua Tenenbaum.

I haven't read this chapter yet myself but will update this answer when I have.

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