/* 

  Mixture of Gaussian in Picat.

  From BLOG example/mixture-of-gaussian.blog
  """
  A model for mixture of Gaussian distribution. 
  The latent variable \verb|z| determines the mixture component of \verb|x|. 
  The program asks the possible value of \verb|z| given the evidence of \verb|x| being 0.2.
   
  @author leili
  @since 2014-06-16
  """
 
  Cf my Gamble model gamble_mixture_of_gaussian.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.

main => go.

/*
  var : z
  Probabilities:
  1: 0.5237410071942447
  0: 0.4762589928057554
  mean = 0.523741

*/
go ?=>
  reset_store,
  run_model(1_000_000,$model,[show_probs_trunc,mean]),
  nl,
  show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  Z = bern(0.5),
  X = cond(Z == 1, normal_dist(0.5,1.0),normal_dist(-0.5,1.0)),

  observe(abs(X-0.2) <= 0.001),
  if observed_ok then
    add("z",Z),
  end.