For several years now, Michael Lee and I have been working on a course book about Bayesian graphical modeling. This book is used to teach graphical modeling courses at UCI and UvA.
After working through the examples provided in this book, you should be able to use the WinBUGS program to build your own Bayesian models, apply them to your own data, and draw your own conclusions.
The book is based on three principles.
The first is that of accessability: the book's only prerequisite is that you know how to operate a computer; you do not need any advanced knowledge of statistics or mathematics. The second principle is that of applicability: the examples in this book are meant to illustrate how Bayesian modeling can be useful for problems that people in cognitive science care about. The third principle is that of practicality: this book offers a hands-on, "just do it" approach, one that we feel keeps students interested and motivated to learn more.
Note: the book is still undergoing development, so any feedback you have is greatly appreciated. The latest version of the book is available for download HERE. Almost all of the examples come with Matlab and R code, available for download here.