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Has anyone created on WinBUGS (Bayesian inference Using Gibbs Sampling) interface with Mathematica similar to BugsXLA for Excel? I'd like to setup the model, define the evidence in a notebook and then analyze the results of the MCMC (Markov chain Monte Carlo) runs.

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Mathematica can do a lot of the necessary tricks natively. A v6 implementation of similar functionality can be found here. The v8 capabilities in the Probability area and wrt distributions have grown enormously. –  Sjoerd C. de Vries Jul 16 '12 at 9:06
Agreed. I would like to use Mathematica's probability functions to fit the posterior data produced by WinBUGS and transform into an empirical distribution. –  Clay Smith Jul 17 '12 at 19:52
I'm using RLink now to call R and run rjags and LaplacesDemon. It's easy to export the chains back into Mathematica. You might want to try RLink to call R2WinBUGS. Unfortunately, I don't have Windows or I would provide you with a starter template. –  Eric Brown Dec 5 '12 at 4:47

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Note that Mathematica 9 features built-in support for R and automated support for simulation of Markov chains and queues.

Perhaps one can perform the entire computation now entirely within Mathematica.

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I would really like to see some examples of Bayesian calculations with Markov chains! Do you have any? –  Eric Brown Dec 5 '12 at 4:48
Examples would, e.g. from the WINBUGS sets would be very instructive. –  ubpdqn Dec 5 '12 at 8:03

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