/* 

  True skill Poisson Binomial in Picat.

  From SPPL model trueskill-poisson-binomial.pynb

  Cf my Gamble model gamble_trueskill_poisson_binomial.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.

/*

  use_observation = false
  var : perfA1
  Probabilities (truncated):
  89: 0.0455000000000000
  91: 0.0444000000000000
  92: 0.0425000000000000
  90: 0.0408000000000000
  .........
  124: 0.0001000000000000
  123: 0.0001000000000000
  121: 0.0001000000000000
  57: 0.0001000000000000
  mean = 90.0855

  var : perfB1
  Probabilities (truncated):
  91: 0.1358000000000000
  90: 0.1309000000000000
  92: 0.1179000000000000
  89: 0.1170000000000000
  .........
  79: 0.0005000000000000
  78: 0.0003000000000000
  99: 0.0001000000000000
  76: 0.0001000000000000
  mean = 90.0033

  var : result
  Probabilities:
  0: 0.5216000000000000
  1: 0.4784000000000000
  mean = 0.4784

  var : skillA
  Probabilities (truncated):
  98: 0.0425000000000000
  104: 0.0414000000000000
  103: 0.0400000000000000
  101: 0.0398000000000000
  .........
  132: 0.0001000000000000
  67: 0.0001000000000000
  63: 0.0001000000000000
  60: 0.0001000000000000
  mean = 100.051

  use_observation = true
  var : perfA1
  Probabilities (truncated):
  74: 0.1562500000000000
  77: 0.1250000000000000
  75: 0.1250000000000000
  78: 0.0937500000000000
  .........
  69: 0.0625000000000000
  79: 0.0312500000000000
  76: 0.0312500000000000
  68: 0.0312500000000000
  mean = 74.21875

  var : perfB1
  Probabilities:
  80: 0.5000000000000000
  78: 0.3125000000000000
  79: 0.0937500000000000
  77: 0.0937500000000000
  mean = 79.0

  var : result
  Probabilities:
  0: 1.0000000000000000
  mean = 0.0

  var : skillA
  Probabilities (truncated):
  86: 0.1250000000000000
  83: 0.1250000000000000
  81: 0.0937500000000000
  80: 0.0937500000000000
  .........
  92: 0.0625000000000000
  88: 0.0625000000000000
  84: 0.0625000000000000
  82: 0.0312500000000000
  mean = 83.03125


*/
go ?=>
  member([UseObservation,NumRuns],[[false,10_000],[true,100_000]]),
  
  println(use_observation=UseObservation),
  reset_store,
  run_model(NumRuns,$model(UseObservation),[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(UseObservation) =>

  PerfB1 = binomial_dist(100,0.9),
  SkillA = poisson_dist(100),
  PerfA1 = binomial_dist(SkillA,0.9),

  Result = cond(PerfA1 > PerfB1,1,0),

  if UseObservation == true then
    observe(PerfB1 <= 80),
    observe( (SkillA >= 77, SkillA < 125)),
    observe(Result == 0)
  end,
  
  if (UseObservation == false) ; ( UseObservation == true, observed_ok) then
    add("perfB1",PerfB1),
    add("skillA",SkillA),
    add("perfA1",PerfA1),
    add("result",Result),
  end.