I am new to WinBUGS and OpenBUGS. I just ran an example model, and am wondering whether I can get the predictions generated by WinBUGS/OpenBUGS. If not, is there any convenient way to achieve this (e.g. with the help of other applications such as R)?
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Yes, you can. In Bayesian tools, it is very easy to get predictions. In your design matrix, just add new rows, with response variable set to NA. You can see concrete example here.