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I am working on a GARCH estimation with a slight twist. For that I need to use a modified posterior distribution as prior for something else. The posterior distribution from Stan is a sample of vectors. I was wondering if there is some way to take a KDE of these samples and feed it to a Stan model to use as posteriors?

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  • $\begingroup$ Can’t you combine the previous model with the “something else” model, to build a single, hierarchical one? The problem would disappear. Generally there’s no nice solutions for using MCMC posterior samples as a prior for next model. $\endgroup$
    – Tim
    Feb 14 at 9:15
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I think using a multivariate normal, multivariate student t, etc. would be a better choice for a prior distribution that approximates a previous posterior distribution, although you may be to obtain the parameters in the unconstrained space. These multivariate distributions are implemented in Stan, whereas kernel density estimators are not. Also, getting reasonable kernel density estimates in a high dimensional parameter space is difficult.

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  • $\begingroup$ The problem is the posterior looks nothing like multivariate normal or student t. Its a GARCH model so kde is not a problem since there are only 3 parameters. I checked with sklearn implementation of kde also. $\endgroup$ Apr 5 '18 at 6:57
  • $\begingroup$ Even in the unconstrained parameter space? $\endgroup$ Apr 6 '18 at 16:13

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