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/* 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 4.04.0 in a model of transcripts of students from the USA (GPA's from 0.00.0 to 4.04.0 and India (GPA's from 0.00.0 to 10.010.0) 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 */ :- use_module(library(mcintyre)). :- if(current_predicate(use_rendering/1)). :- use_rendering(c3). :- endif. :- mc. :- begin_lpad. is_density_A:0.95;is_discrete_A:0.05. % the probability distribution of GPA scores for American students is % continuous with probability 0.95 and discrete with probability 0.05 agpa(A): beta(A,8,2) :- is_density_A. % the GPA of American students follows a beta distribution if the % distribution is continuous american_gpa(G) : discrete(G,[4.0:0.85,0.0:0.15]) :- is_discrete_A. % the GPA of American students is 4.0 with probability 0.85 and 0.0 with % probability 0.15 if the % distribution is discrete american_gpa(A):- agpa(A0), A is A0*4.0. % the GPA of American students is obtained by rescaling the value of agpa % to the (0.0,4.0) interval is_density_I : 0.99; is_discrete_I:0.01. % the probability distribution of GPA scores for Indian students is % continuous with probability 0.99 and discrete with probability 0.01 igpa(I): beta(I,5,5) :- is_density_I. % the GPA of Indian students follows a beta distribution if the % distribution is continuous indian_gpa(I): discrete(I,[0.0:0.1,10.0:0.9]):- is_discrete_I. % the GPA of Indian students is 10.0 with probability 0.9 and 0.0 with % probability 0.1 if the % distribution is discrete indian_gpa(I) :- igpa(I0), I is I0*10.0. % the GPA of Indian students is obtained by rescaling the value of igpa % to the (0.0,4.0) interval nation(N) : discrete(N,[a:0.25,i:0.75]). % the nation is America with probability 0.25 and India with probability 0.75 student_gpa(G):- nation(a),american_gpa(G). % the GPA of the student is given by american_gpa if the nation is America student_gpa(G) :- nation(i),indian_gpa(G). % the GPA of the student is given by indian_gpa if the nation is India :- end_lpad. /** <examples> ?- mc_lw_sample(nation(a),student_gpa(4.0),1000,PPost). % probability that the nation is America given that the student got 4.0 % in his GPA % expected result: 1.0 ?- mc_sample(nation(a),1000,PPrior). % prior probability that the nation is America % expected result: 0.25 */