/* 

  Indian GPA problem in Picat.

  From cplint http://cplint.ml.unife.it/example/inference/indian_gpa.pl
  """
  The Indian GPA Problem. From 
  http://www.robots.ox.ac.uk/~fwood/anglican/examples/viewer/?worksheet=indian-gpa 
  "This example was inspired by Stuart Russell...the problem is: if you observe 
  that a student GPA is exactly 4.0 in a model of transcripts of students 
  from the USA (GPA's from 0.0 to 4.0 and India (GPA's from 0.0 to 
  10.0) what is the probability that the student is from India?... 
  As we know from statistics, given the mixture distribution and given the 
  fact that his/her GPA is exactly 4.0, the probability that the student 
  is American must be 1.0.
  (i.e. zero probability that the student is from India)."
  Probabilistic logic program from 
  https://github.com/davidenitti/DC/blob/master/examples/indian-gpa.pl
  """

  Cf my Gamble model gamble_indian_gpa.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.

/*

  * Observe GPA 4.0 
    var : gpa
    Probabilities (truncated):
    4.0: 0.9794959419051688
    3.99933292902975: 0.0004271678769757
    3.999222703277703: 0.0004271678769757
    3.999128492548656: 0.0004271678769757
    .........
    3.991430761288587: 0.0004271678769757
    3.990117294709253: 0.0004271678769757
    3.99005961790218: 0.0004271678769757
    3.990041163745355: 0.0004271678769757
    mean = 3.99989

    var : nationality
    Probabilities:
    usa: 0.9944468175993165
    india: 0.0055531824006835
    mean = [usa = 0.994447,india = 0.00555318]

    var : perfect
    Probabilities:
    true: 0.9794959419051688
    false: 0.0205040580948313
    mean = [true = 0.979496,false = 0.0205041]


  * Observe perfect
    var : gpa
    Probabilities:
    4.0: 0.6104205236709865
    10.0: 0.3895794763290135
    mean = 6.33748

    var : nationality
    Probabilities:
    usa: 0.6104205236709865
    india: 0.3895794763290135
    mean = [usa = 0.610421,india = 0.389579]

    var : perfect
    Probabilities:
    true: 1.0000000000000000
    mean = [true = 1.0]

  * Observe GPA 3.0

    var : gpa
    Probabilities (truncated):
    3.009967493363641: 0.0136986301369863
    3.009857760281236: 0.0136986301369863
    3.009483848237192: 0.0136986301369863
    3.009308582641794: 0.0136986301369863
    .........
    2.991065863981408: 0.0136986301369863
    2.990856581828956: 0.0136986301369863
    2.99071886250317: 0.0136986301369863
    2.990261559835757: 0.0136986301369863
    mean = 2.99981

    var : nationality
    Probabilities:
    usa: 0.6849315068493150
    india: 0.3150684931506849
    mean = [usa = 0.684932,india = 0.315068]

    var : perfect
    Probabilities:
    false: 1.0000000000000000
    mean = [false = 1.0]

  * Observe GPA 4.1

    var : gpa
    Probabilities (truncated):
    4.109083606912328: 0.0400000000000000
    4.108320150574818: 0.0400000000000000
    4.108249672738951: 0.0400000000000000
    4.106630577755454: 0.0400000000000000
    .........
    4.092139552390267: 0.0400000000000000
    4.090959901963807: 0.0400000000000000
    4.090655261692896: 0.0400000000000000
    4.090297838715044: 0.0400000000000000
    mean = 4.10021

    var : nationality
    Probabilities:
    india: 1.0000000000000000
    mean = [india = 1.0]

    var : perfect
    Probabilities:
    false: 1.0000000000000000
    mean = [false = 1.0]

  * Observe nationality = usa

    var : gpa
    Probabilities (truncated):
    4.0: 0.1568432890123702
    3.999496482312445: 0.0000661506912747
    3.999053506180203: 0.0000661506912747
    3.99875643849315: 0.0000661506912747
    .........
    0.001365123317281: 0.0000661506912747
    0.001136243343882: 0.0000661506912747
    0.001012198627466: 0.0000661506912747
    0.000850087032118: 0.0000661506912747
    mean = 2.30806

    var : nationality
    Probabilities:
    usa: 1.0000000000000000
    mean = [usa = 1.0]

    var : perfect
    Probabilities:
    false: 0.8431567109876298
    true: 0.1568432890123702
    mean = [false = 0.843157,true = 0.156843]

  * Observe nationality = india
    var : gpa
    Probabilities (truncated):
    10.0: 0.0998320456835741
    9.999500494450098: 0.0000671817265704
    9.99838771764114: 0.0000671817265704
    9.997837655245251: 0.0000671817265704
    .........
    0.003043222242521: 0.0000671817265704
    0.00295476056773: 0.0000671817265704
    0.002480130643807: 0.0000671817265704
    0.000008367933337: 0.0000671817265704
    mean = 5.48861

    var : nationality
    Probabilities:
    india: 1.0000000000000000
    mean = [india = 1.0]

    var : perfect
    Probabilities:
    false: 0.9001679543164259
    true: 0.0998320456835741
    mean = [false = 0.900168,true = 0.099832]


*/
go ?=>
  reset_store,
  run_model(30_000,$model,[show_probs_trunc,mean]),
  nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  %  Note: In https://probprog.github.io/anglican/examples/viewer/?worksheet=indian-gpa
  %        the proportions are a little different.
  % Nationality = categorical([0.75,0.25],["india","usa"]),
  Nationality = categorical([0.5,0.5],["india","usa"]),

  Perfect = cond(Nationality == "india",
                  flip(0.10),
                  flip(0.15)),

  GPA = cond(Nationality == "india",
              condt(Perfect,
                    10.0,
                    uniform(0,10)),
              condt(Perfect,
                    4.0,
                    uniform(0,4))),
 
  % Observations:
  observe((GPA <= 4.0, abs(GPA-4.0) <= 0.01)), % Observe GPA=4.0
  % observe(abs(GPA-3.0) <= 0.01), % Observe GPA=3.0
  % observe(abs(GPA-4.1) <= 0.01), % Observe GPA=4.1
  % observe(Perfect),
  % observe(not Perfect),
  % observe(Nationality == "usa"),
  % observe(Nationality == "india"),  
  
  if observed_ok then
    add("nationality",Nationality),
    add("perfect",Perfect),
    add("gpa",GPA),        
  end.