There’s an example how to compute the marginal posterior for k in my post in the thread Stochasticity in pareto-k diagnostics over different fitting runs - #5 by avehtari. Form that marginal you can infer the expected amount of variability. You can reduce the variability by running longer chains, or you can make importance weights better behaving (and thus getting lower k’s) with moment matching loo Avoiding model refits in leave-one-out cross-validation with moment matching • loo
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