Keith: In my reply to Tim’s question in the Stan forum, I suggested using logarithmic pooling (https://link.springer.com/content/pdf/10.1007/BF00140056.pdf) to combine the posteriors. Now that of course opens up the can of worms of choosing the weights with which to aggregate the distributions, but I think it could be a valuable pursuit.

]]>One of the primary roles of multiverse analyses may be to assess if some findings are common among the differing analysis (e.g. treatment effect always positive). Similar to meta-analysis where the most important step is to anticipate and critically assess what should be common in the different studies. (Even though the https://en.wikipedia.org/wiki/Meta-analysis entry puts it as _In addition to_ providing an estimate of the unknown common truth – its primary.)

Interestingly stacking is “ideal when the K different models being fit have nothing in common”!

Similar (harder) challenges arise with _combining_ multiple priors literature from 1980,s (e.g. Aggregating opinions through logarithmic pooling) which I know some folks are now trying to recast.

Given multiple posteriors are tomorrow’s multiple priors that perspective might be helpful. For instance, Multiple experts. Mathematical and behavioural aggregation. Pooling methods. http://tonyohagan.co.uk/academic/eliccourse.html

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