I am interested in fitting a Bayesian Two Factor ANOVA in BUGS or by utilizing some R package. Unfortunately I am having a hard time finding resources on this topic. Any suggestions? Even an article describing the approach would be helpful.
Simon Jackman has some working code for fitting ANOVA and regression models with JAGS (which is pretty like BUGS), e.g. two-way ANOVA via JAGS (R code) or maybe among his handouts on bayesian analysis for the social sciences.
A lot of WinBUGS code, including one- and two-way ANOVA, seem to be available on the companion website for Bayesian Modeling Using WinBUGS: An introduction.
I'm a bit late to the show here, but John Kruschke's recently published book
Doing Bayesian Data Analysis: A Tutorial with R and BUGS has a whole chapter (19) on this. His book is written in a highly accessible and practical style, well worth checking out for his description of the approach. He also includes R and BUGS code for his examples.
His website accompanying the book is interesting reading also: http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/ and includes all the code in the book.
See Chapter 10 of Marc Kery's book Introduction to WinBUGS for Ecologists, where he compares a two-way ANOVA in R with several versions of the model in WinBUGS. (The book has lots of great examples; ecology not a pre-requisite.) Website for the book is here: http://www.mbr-pwrc.usgs.gov/software/kerybook/