Using Multivariate Posterior Samples as Prior in Julia’s Turing for MCMC

General Usage
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Question:

I would like to use posterior distribution samples obtained via MCMC for multivariate parameters of a certain model as the prior distribution when running MCMC on another dataset.

Currently, for the univariate case, I have been able to set the prior distribution by performing kernel density estimation (KDE) using the code from the following URL:How to Use a Distribution Estimated via Kernel Density Estimation (KDE) as a Prior in Turing.jl

However, I realized that using univariate KDE on the posterior samples of the parameters causes the correlations between parameters to be lost. Therefore, I am considering using multivariate KDE to approximate the sample distribution as a probability distribution and use it as the prior distribution in Julia’s Turing for MCMC.

Specifically, I need help with the following points:

  1. Estimating Multivariate Distributions: How can I accurately estimate a multivariate distribution from posterior samples using multivariate KDE?

  2. Integrating with Turing: What are the specific steps or code examples for setting the estimated multivariate distribution as a prior in Julia’s Turing?

  3. Maintaining Parameter Correlations: What are the best practices or considerations to properly maintain the correlations between parameters when using multivariate KDE?

Any guidance on implementation methods, reference materials, or code examples would be greatly appreciated.