/* 

  Color of the taxi in Picat.

  From https://www.bayesia.com/2018-03-02-probabilistic-reasoning-under-uncertainty

  Originally from Kahnemann, Slovic, Tversky "Judgement under uncertainty"
  

  There has been an accicent involving a taxi.
  There are two kinds of taxis:
    - yellow taxi: 85% 
    - white taxi: 15%

  A witness say: It was a white taxi involved in the accident.

  Researcher:
    - 80% of all witness statements are true
    - 20% of all witness statements are false.

  What is the probability that it was a white taxi involved in
  the accident?

  Cf my Gamble model gamble_color_of_the_taxi.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.

/*

  Answer: The probability that it was a white taxi involved in the accident
          is about 41%. And it's the same as in the talk.

  var : involved
  Probabilities:
  yellow: 0.5801396695622552
  white: 0.4198603304377448
  mean = [yellow = 0.58014,white = 0.41986]

  var : witness white
  Probabilities:
  false: 0.5520354283767671
  true: 0.4479645716232328
  mean = 0.447965

  var : witness yellow
  Probabilities:
  true: 0.5460739226707546
  false: 0.4539260773292454
  mean = 0.546074


*/
go ?=>
  reset_store,
  run_model(20_000,$model,[show_probs_trunc,mean % ,
                           % use_local_tabling=true
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
% Witness says color but is is only x percent reliable.
% Witness experts states that a witness can only be 80% reliable
% (given the same circumstances as the accidents).
% table
witness(C,Involved) = cond(Involved == C, flip(8/10),flip(2/10)).

model() =>
  
  % Prior distributions of the different taxis.
  Involved = categorical([15/100,85/100],[white,yellow]),
  
  observe(witness(white,Involved)),

  if observed_ok then
    add("involved",Involved),
    add("witness white",witness(white,Involved)),
    add("witness yellow",witness(yellow,Involved)),    
  end.