I’ll add non-MCMC analysis to this system. Now we have only ADVI, but we may have something else later, but all distributional approximations can use the new Pareto diagnostic. Given draws theta^{(s)} from any distributional approximation q, and log(q(theta^{(s)})) and log(p(theta^{(s)})) we can compute Pareto k (khat) and effective sample size (N_eff) estimates. These should be reported in every interface similarly as Rhat and N_eff are reported for HMC/NUTS.