The idea behind separating StanFit from StanAnalyze is the users may be interested just in our convergence diagnostics and stuff (i.e. in the Stan services) but are not actually using Stan to fit their models. On the R side, we have also discussed a package that makes it easier to work with MCMC samples and transform them to various formats relevant in different applications. This package may or may not be identical to StanAnalyze. In any case, I think we should separate the Stan fitting specific stuff from the general diagnostics we have developed that also work for samples generated with software other than Stan.
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