Composing Stan models (posterior as next prior)

[bgoodri]

@anon75146577 was lamenting about the same thing on Twitter the other day. For the univariate case, a very good solution that has not been utilized is to use quantile parameterized distributions for priors that I linked to at

Elicitation observation models

I don’t have a reference or any experience doing this, but I have always believed the quantile function is the easiest thing to elicit with. I talked about this a little bit on pages 8 – 10 of https://mc-stan.org/workshops/Rmedicine2018/ . Basically, there are these quantile parameterized distributions — which are distributions whose parameters are quantiles — that I implemented in “Helper functions”. So, you can asked the purported expert things like “What would be your over / under (median) on…

in which case the posterior quantiles become the hyperparameters for the prior the next time your have new data to condition on. In the multivariate but unconstrained case, you could link the together with a multivariate normal copula density, which is sort of alluded to starting at page 38 of http://www.metalogdistributions.com/images/TheMetalogDistributionsInvitedLecture.pdf . For things like simplexes that are multivariate but constrained, I don’t know that there is a great solution.