Can traces be used as priors?

[chartl]

So there’s a notebook on updating priors:

https://docs.pymc.io/notebooks/updating_priors.html

and a couple discussions on the forums for how to do this in a multivariate way either approximately:

Updating multivariate priors

Dear all, There’s a very helpful notebook on Updating Priors in which the prior distributions of three variables are updated as new data becomes available. Importantly, these prior distributions are assumed independent. In practice however, priors are often correlated. How would one consider such a case? From what I’ve seen, the “Interpolated” distribution is only applicable to univariate problems, and I have not seen any examples of multivariate distributions being updated as in the above not…

or using copulas

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: …