/* 

  A/B test simple in Picat.

  Simple A/B test.

  Cf my Gamble model gamble_ab_test_simple.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 : rate A
  Probabilities (truncated):
  0.325794485218949: 0.0060240963855422
  0.254575746612066: 0.0060240963855422
  0.249143484957635: 0.0060240963855422
  0.240038150669684: 0.0060240963855422
  .........
  0.010887663009898: 0.0060240963855422
  0.007450712348583: 0.0060240963855422
  0.006648806052436: 0.0060240963855422
  0.001519299939476: 0.0060240963855422
  mean = 0.0971197

  var : rate B
  Probabilities (truncated):
  0.246583752581517: 0.0060240963855422
  0.190796939187728: 0.0060240963855422
  0.182072401584263: 0.0060240963855422
  0.179440631356682: 0.0060240963855422
  .........
  0.007763800668381: 0.0060240963855422
  0.006732126104081: 0.0060240963855422
  0.005904895027853: 0.0060240963855422
  0.001565219137154: 0.0060240963855422
  mean = 0.0706578

  var : diff
  Probabilities (truncated):
  0.170756961713498: 0.0060240963855422
  0.149034887617863: 0.0060240963855422
  0.148882707750458: 0.0060240963855422
  0.135884629066641: 0.0060240963855422
  .........
  -0.197447606953484: 0.0060240963855422
  -0.204612726113614: 0.0060240963855422
  -0.211581473262455: 0.0060240963855422
  -0.292422826706721: 0.0060240963855422
  mean = -0.0264618

  var : diff > 0.0
  Probabilities:
  0: 0.6265060240963856
  1: 0.3734939759036144
  mean = 0.373494


*/
go ?=>
  reset_store,
  run_model(100_000,$model,[show_probs_trunc,mean]),
  nl,
  show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  NA = 20, % Number of trials for A
  NB = 25, % Number of trials for B

  RateA = beta_dist(1,1),
  RateB = beta_dist(1,1),  

  SA = binomial_dist(NA,RateA),
  SB = binomial_dist(NB,RateB),  

  Diff = RateB - RateA,

  observe(SA == 1, SB == 1), % Number of successes for A and B
  
  if observed_ok then
    add("rate A",RateA),
    add("rate B",RateB),
    add("diff",Diff),
    add("diff > 0.0",cond(Diff > 0, 1,0))
  end.