/* 

  Size of material in Picat.

  https://pedrozudo.github.io/docs/20_thesis/thesis_final_online_compressed.pdf
  page 100
  """
  Example 6.11. We model the size of a ball as a mixture of different beta distributions,
  depending on whether the ball is made out of wood or metal (Line 1)4. We would
  now like to know the probability of the ball being made out of wood given that we
  have a measurement of the size of the ball. In order to condition on a continuous
  random variable we introduce the observation/2 predicate, which has an analogous
  functionality as the evidence predicates for Boolean random variables.
  1 3/10::material(wood);7/10::material(metal).
  2
  3 size~beta(2,3):-material(metal).
  4 size~beta(4,2):-material(wood).
  5
  6 observation(size,4/10).
  7 query(material(wood)).
  """

  Cf my Gamble model gamble_size_of_material.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.

/*

  var : material
  Probabilities:
  metal: 0.8610000000000000
  wood: 0.1390000000000000
  mean = [metal = 0.861,wood = 0.139]
  HPD intervals:
  show_hpd_intervals: data is not numeric

  var : size
  Probabilities (truncated):
  0.400997296297817: 0.0010000000000000
  0.40099693633027: 0.0010000000000000
  0.400996650951801: 0.0010000000000000
  0.400995567975159: 0.0010000000000000
  .........
  0.399002571247472: 0.0010000000000000
  0.399001677083766: 0.0010000000000000
  0.399001473749497: 0.0010000000000000
  0.39900105434383: 0.0010000000000000
  mean = 0.399999
  HPD intervals:
  HPD interval (0.9): 0.39922140219196..0.40099729629782
  HPD interval (0.95): 0.39900105434383..0.40089271816347
  HPD interval (0.99): 0.39900105434383..0.40097725278882


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,
                           % show_percentiles,
                           show_hpd_intervals,hpd_intervals=[0.9,0.95,0.99],
                           % show_histogram,
                           min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  MaterialType = [wood,metal],
  Material = categorical([3/10,7/10],MaterialType),

  Size = cond(Material == metal, beta_dist(2,3), beta_dist(4,2)),
  
  observe(abs(Size-(4/10)) < 0.001),

  if observed_ok then
    add("material",Material),
    add("size",Size)
  end.