can sbc used to adjust prior mean if rank histograms are biased?
For example from user manual, 25.5.3 When Stan’s sampler goes wrong, the last plot of theta_sim[1] ranks shows that simulated values are much smaller than the values fit from the data. If so, can giving a higher prior mean be a solution, at least make rank plot better?
SBC is evaluating if the inference algorithm is working and that will be a function of where in parameter space the sampler ends up.
Like, if the eight schools example was done in a part of parameter space that didn’t have a funnel (the measurement errors were tiny on all the individual school measurements relative to the scales of the measurements themselves), then the centered parameterization would be fine, and SBC would presumably say everything is working.