WebPPL Hidden Markov Model Inference

unfair-casino-hmm.js

/*
Dealer repeatedly flips a coin. Sometimes the coin is fair, with P(heads) = 0.5,
sometimes it’s loaded, with P(heads) = 0.8. Dealer occasionally switches coins,
invisibly to you. Given an list of observed coin flips, infer if the coin was
fair for each individual flip.
*/

var hmm = function(n, initial, transitionf, observef) {
  var impl = function(N) {
    if (N > 1) {
      var state = impl(N - 1)
      var next_hidden = transitionf(state.hidden[state.hidden.length - 1])
      var next_observed = observef(next_hidden)
      return { hidden: state.hidden.concat([next_hidden]), observed: state.observed.concat([next_observed]) }
    }
    else return { hidden: [initial], observed: [observef(initial)] }
  }
  return impl(n)
}

var sometimes_change_coin = function(previous_fair_state) {
  return flip(0.9) ? previous_fair_state : !previous_fair_state
}

var do_flip = function(is_fair) {
  var is_head = is_fair ? flip(0.5) : flip(0.8)
  return is_head ? "H" : "T"
}

var post = Infer({method: 'MCMC', samples: 1000, lag: 100, burn: 50,
                  model: function() {
  var data = ["H", "H", "H", "H", "H", "H", "T", "H", "T", "H", "T", "H", "T"]
  var model = hmm(data.length, flip(0.5), sometimes_change_coin, do_flip)
  condition(sum(map2(function(a, b) { return a == b}, data, model.observed)) == data.length)
  return model.hidden
}})
viz.marginals(post)