Using MCMC based model in closed loop

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Would something like this work for you?

Prior propagation by nonparametric copulas

Having participated in a number of conversations regarding updating priors, I thought about the best one could do when you observe only a sample \hat \theta_k \sim \theta | D_1, \dots, D_k; and seek to compute P[\theta|D_1, \dots, D_{k+1}]. In effect, the question is how to extend https://docs.pymc.io/notebooks/updating_priors.html in some reasonable way for multivariate parameters. Previous topics have suggested using multiple pm.Interpolated distributions: or parametric approximations: …

It was your initial question which prompted me to play around with it a bit; and it’s the closest I could come to constraining a new trace by an old trace.