Add a logdensity specialization that takes NamedTuples

[Red-Portal]

As discussed on Slack, it would be good to have an additional specialization of logdensity that takes NamedTuple-valued inputs. The Turing main repo already implements this as boilerplate for AdvancedMH, so it would be nice to have an official unified implementation that also supports AD.

Right now, it seems to me that adding a specialization to unflatten would do the job. (And maybe change the function's name to something else since it is not doing unflatten anymore?)

[devmotion]

A prior discussion (I don't remember the details): #501

[Red-Portal]

Hi @yebai , could chime in on what we should do here?

[yebai]

There are other parts of AbstractMCMC that would benefit from a more general form of logdensity (ℓ, ...) which doesn't assume the second argument is a vector of reals, so it is worth considering how we can consistently handle this. We should probably take a look at something more recent for specifying interfaces and see whether we could have a LogDensityProblem 2.0:

https://github.com/rafaqz/Interfaces.jl

cc @willtebbutt and @sunxd3

[Red-Portal]

@devmotion Any additional thoughts?