Swifty MCMC and python iterop

[dellaert]

We should think/talk about MCMC algorithm API and tfp interop.

@marcrasi says:

As a direct translation of the Python API, the current API looks right to me. If you want to go this direction, then that sounds good to me!

---

The "Swifty" way can make some things a lot nicer so I'll describe a "Swifty" idea here to tempt you :)

The TransitionKernel looks like an infinite Sequence. So there's no need to define a protocol TransitionKernel -- you can conform things to Sequence instead.

For example, RandomWalkMetropolis would be something like:

struct RandomWalkMetropolis<State>: Sequence, IteratorProtocol {

  var previousLogProb: Double
  var currentState: State

  let target_log_prob_fn: (State) -> Double
  let new_state_fn : (State)->State

  init(_ target_log_prob_fn: @escaping (State) -> Double, _ new_state_fn : @escaping (State)->State, _ initialState: State) {
    ...
  }

  mutating func next() -> State {
    let result = currentState

    // update `currentState` and `previousLogProb` according to metropolis rules
    ...

    return result
  }
}

This is nice because it allows us to use all the Sequence algorithms. For example, sampleChain becomes something like:

Array(sequence.dropFirst(num_burnin_steps).prefix(num_results))

Originally posted by @marcrasi in https://github.com/borglab/SwiftFusion/pull/95/files

[marcrasi]

I'll add an agenda item for this to our Friday meeting!

[dabrahams]

While we're in this area, consider #143