For exercise 3, there should not be bounds on the regression coefficients. normal(0, 10) is going to be a wide prior for sensible logistic regression intercepts, but for slopes, informativeness depends on the scale of the predictors.

For 99% intervals you need roughly 200 times as many draws (because you need to estimate a 0.5% quantile), so we usually recommend narrower posterior intervals to measure calibration using posterior predictive checks.

P.S. It’s “Stan”, not “STAN”, because it’s not an acronym.

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