Pooling or stacking?

[maxbiostat]

For background, see this discussion. I proposed LP could be a way of combining many posteriors. Aki Vehtari points to his paper on stacking distributions.

My question is: should someone look into comparing a choice of the weights in LP that minimises, say, the KL distance to the true model, a bit like Rufo, Martin & Perez did? My idea would be to take the examples from Aki's paper and directly compare LP and stacking.

Not something for now, just maybe a project to keep in mind for the future, @fccoelho @lsbastos @DVMath