Update AdvancedPS to match SSMProblems interface

[THargreaves]

Draft work on updating AdvancedPS to match the SSMProblems interface.

To run this code you need to dev SSMProblems in the AdvancedPS environment and dev AdvancedPS in the examples/particle-gibbs environment.

[yebai]

This feels a bit redundant with transition!!. Consider merging these into the function transition!!.

[FredericWantiez]

The main issue here is that AbstractMCMC does not forward data explicitly, it just assumes the obervables are internal to the model

[THargreaves]

I see. One way around this would be to define something like

struct ConditionedSSM
    ssm::AbstractStateSpaceModel
    observations::Vector{Vector{Float64}}
end

though that's one more bit of API bloat.

[yebai]

I like the idea; it is also how the condition mechanism works for DynamicPPL models.

[FredericWantiez]

Doesn't have to be nested, or another type, as long as these are defined by the user:

function emission_logensity(model::AbstractStateSpaceModel, state, step::Int) 
   return logpdf(Normal(state), observations[step]) # Global scope
end

or

function emission_logensity(model::AbstractStateSpaceModel, state, step::Int) 
   return logpdf(Normal(state), model.observations[step]) 
end

It's a bit what model() | (; y=observations) would do in DynamicPPL

[FredericWantiez]

That would make backward compatibility with Libtask quite difficult @yebai

[yebai]

@THargreaves can you revert this change for now? It will take a bit more work on the Turing side before we can do it.