“… we derive a variational model to accommodate the non-conjugate
LKJ prior [12], allowing the user to model the covariance and marginal
variances separately. Specifically, we use…”

This reminds me of a question I had been wondering about. If you draw once from the prior predictive distribution for each of your N observations and call loo() using these prior predictive outcomes rather than the actual outcomes, do the estimated generalized Pareto parameters tell you about the sensitivity of your posterior to your prior?

I don’t understand the question. Generalized Pareto shape parameter is for the IS (raw) weight distribution. In LOO the (raw) weights are proportional to p(theta^{(s)} | y_{-i})/p(theta^{(s)} | y), where theta^{(s)} are samples from the posterior p(theta | y). I don’t understand how sampling from the prior predictive distribution would fit in here. Can you explain more what do you mean?