Using bayeux to organize numpyro models and access features

[SamuelBrand1]

@dylanhmorris has put me onto bayeux. I think this would be a useful addition.

bayeux has some handy features:

• A from_numpyro method that coverts a numpyro model into a bayeux model object.
• bayeux models have a debug mode https://jax-ml.github.io/bayeux/debug_mode/ which covers Adding stress testing utility for model inference to help isolate cause of stochastic failure in inference #197 and makes Adding stresstest function to MechanisticInferer #199 obsolete.
• bayeux models can be cast to other libraries, e.g. optimistix which can find their MAP values (which can be handy).

[dylanhmorris]

Passing along credit: @damonbayer put me onto bayeux

[SamuelBrand1]

As of #248 we have access to bayeux debug. Do we want to use any other package integrations (e.g. MAP opt to start in a high probability mass region for NUTS), or is this issue closed?

[arik-shurygin]

tagging this issue as wontfix for now, I think more investment is needed to unlock the usefulness of the bayeux debugging. Unfortunately there are many other high priority items on the docket as well.