Support for multiple initial conditions, replicates, and partial pooling.

[saumil-sh]

Hey,
I use turing_interface from this package in my project. I could extend the turing_interface to accept multiple initial conditions and replicate (in case of experimental and measured data) for the same ODE system (complete pooling). Some statistical modeling feature partial pooling of inferred parameters, and this extension was also possible.

I made the rookie mistake of upgrading my Julia to v1.10 without considering the consequences. This led to many packages failing on precompile. I managed to hack my way around this by removing the compact. I know this is not ideal.

I am writing a test for this now, and I will also update the documentation at the appropriate places. I don't have stan installed at the moment, so I can't fix failing stan tests at the moment.

Meanwhile, can someone please tell me whether this is a useful and good way to implement the features?

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[saumil-sh]

I realized I am trying to achieve too many things within this pull request, including updating compat to Julia v1.10 and MTK v9. The functionality I want to add has nothing to do with these two. So, I will create a couple of pull requests that are more minimal and modular.

[ChrisRackauckas]

Awesome, I was going to say that will be needed since there's a ton going on here. Indeed splitting the PR will help with the updating and review a lot.