/* 

  Uniform ball in Picat.

  BLOG example/uniform-ball.blog
  """
  Model file for balls in an urn, allowing observation errors. 
  This version uses a Poisson prior for the number of balls.
  """

  Result of the BLOG model:
  """
  Distribution of values for size({b for Ball b : true})
  	1	0.07696467881871667
	2	0.2749155437572819
	3	0.3066400745347743
	4	0.34147970288922114
  Distribution of values for (ballDrawn(Draw[0]) = ballDrawn(Draw[1]))
	false	0.7070034886998044
	true	0.29299651130018706
  """


  Cf my Gamble model gamble_uniform_ball.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.
% import ordset.

main => go.

/*
  Num accepted samples: 1000  Total samples: 475174  (0.002%)

  var : num balls
  Probabilities:
  4: 0.3650000000000000
  3: 0.3070000000000000
  2: 0.2600000000000000
  1: 0.0680000000000000
  mean = 2.969

  var : ball 1 == ball 2
  Probabilities:
  0: 0.7180000000000000
  1: 0.2820000000000000
  mean = 0.282


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           % show_percentiles,show_histogram,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  /*
    """
    Evidence file asserting that the drawn balls appeared blue on half the 
    draws and green on half the draws.
    """
  */
  Data = [true,false,true,false,true,false,true,false],  
  N = 8,

  NumBalls = random_integer1(4),
  IsBlue = flip_n(0.5,N),
  BallDrawn = random_integer1_n(NumBalls,N),
  ObsBlue = [cond(IsBlue[BallDrawn[D]]==true,flip(0.8),flip(0.2))  : D in 1..N],

  observe(Data == ObsBlue),
 
  if observed_ok then
    add("num balls",NumBalls),
    add("ball 1 == ball 2",cond(BallDrawn[1]==BallDrawn[2],1,0))
  end.