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BUGS is an acronym for Bayesian inference Using Gibbs Sampling; BUGS is also a software package for doing this. Use for all versions of BUGS, also WINBUGS and OpenBUGS.

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R only alternatives to BUGS

You can take a look at the MCMCglmm package that comes with very nice vignettes. There's a also a bayesglm() function for fitting Bayesian generalized linear models in the arm package, by Andrew Gelma …
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Bayesian two-factor ANOVA

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 …
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