/* 

  Beta comparison in Picat.

  From infer.net src/tests/Test/BlogTests.cs
  """
  a = Beta(11,500)[mean=0.02153], b = Beta(16,695)[mean=0.0225]
  aGreaterThanConstant = Bernoulli(0.9849)
  P(A > B) =  Bernoulli(0.4467)
  """

  This is an A/B test.

  This is a port of my Racket/Gamble model gamble_beta_comparison.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.

main => go.

/*

  var : ARate
  Probabilities (truncated):
  0.028186066831246: 0.0454545454545455
  0.028086347415719: 0.0454545454545455
  0.027263549591807: 0.0454545454545455
  0.025770386628652: 0.0454545454545455
  .........
  0.016907220867913: 0.0454545454545455
  0.014902729258726: 0.0454545454545455
  0.013514855121266: 0.0454545454545455
  0.011093578306136: 0.0454545454545455

  mean = 0.0203634

  var : BRate
  Probabilities (truncated):
  0.032329959176256: 0.0454545454545455
  0.031241788952231: 0.0454545454545455
  0.030749082505564: 0.0454545454545455
  0.028821906226334: 0.0454545454545455
  .........
  0.014475546752513: 0.0454545454545455
  0.01230742107712: 0.0454545454545455
  0.011615652004552: 0.0454545454545455
  0.011020021786651: 0.0454545454545455

  mean = 0.0211452

  var : ARate > BRate
  Probabilities:
  0: 0.5909090909090909
  1: 0.4090909090909091
  mean = 0.409091

  var : ARate > 0.01
  Probabilities:
  1: 1.0000000000000000
  mean = 1.0

*/
go ?=>
  reset_store,
  run_model(100_000,$model,[show_probs_trunc,mean,
                            presentation=["ARate","BRate","ARate > BRate","ARate > 0.01"]]),
  % fail,  
  nl.
go => true.
  
  
model() =>
  ARate = beta_dist(1,10),
  BRate = beta_dist(1,10),

  ATrialCount = 500,
  BTrialCount = 700,

  ASuccessCount = binomial_dist(ATrialCount,ARate),
  BSuccessCount = binomial_dist(BTrialCount,BRate),

  observe(ASuccessCount == 10, BSuccessCount == 15),
  
  if observed_ok then
    add("ARate",ARate),
    add("BRate",BRate),
    add("ARate > BRate",cond(ARate > BRate,1,0)),
    add("ARate > 0.01",cond(ARate > 0.01,1,0))
  end.