For instance, if I want to compare how well various model specifications cross validate but some models converged with default parameters such the number of iterations, chains, and the treedepth, and others needed adjusting before they converged, are all the model's estimates and validity still comparable? I'm not asking about uniformity of priors between models -- only the number of iterations, chains, the treedepth.
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$\begingroup$ What is "treedepth" in this context? The number of (MCMC?) iterations does not have to be constant across models as this qualifies the convergence of the (Markov?) chain, rather than the goodness of fitting the data. $\endgroup$– Xi'anMar 24 at 8:53