Supporting inputs implementing the LogDensityProblems interface

[sethaxen]

Both DynamicHMC and now also AdvancedHMC (TuringLang/AdvancedHMC.jl#301) support as inputs objects that implement the LogDensityProblems interface. It makes sense then to support as inputs objects that implement the LogDensityProblems interface. We might even consider switching to using LogDensityProblems internally.

I don't think we should switch to using LogDensityProblems internally, mainly because currently the LogDensityProblems API only supports computing the log density and its gradient, while we want to also support optimizers that compute the Hessian.

Turing is starting to use LogDensityProblems under the hood, but to keep support for Hessians, we should probably continue to use its OptimizationFunction.

It might be worth pushing to have Hessian abilities in the LogDensityProblems API.