MCMC and VI implementations

[benjaminpope]

Now that we have grid searches and Absil/Ruffio contrast limits working, we should build interfaces to numpyro and implement

• [x] MCMC, HMC etc
  • Shashank's hierarchical calibration example?
• [ ] SVI - see @hughmcdougall's examples.

[benjaminpope]

Notebook implementation of numpyro NUTS sampling with a BinaryModelCartesian here.

Should the interface to this be:

• a method of OIData calling a model and bounds
• a notebook doc and the numpyro use is necessarily DIY
• some third thing

?

[benjaminpope]

We should use init_to_value in the init_strategy argument in infer.nuts to initialize to the optimum values of a grid search (plus any static parameters we held fixed in the grid search).

I think we should provide

• [ ] a flexible notebook expressing the right way to do this
• [ ] an mcmc(oidata,model,samples_dict,optimized) function to automate this for basic users, where it will take the bounds and any static values from the samples dict. We may have to alter the optimized grid outputs to return richer values (args, and values, and any metadata) to reliably do this.