1/* 2The Indian GPA Problem. From 3http://www.robots.ox.ac.uk/~fwood/anglican/examples/viewer/?worksheet=indian-gpa 4"This example was inspired by Stuart Russell...the problem is: if you observe 5that a student GPA is exactly 4.04.0 in a model of transcripts of students 6from the USA (GPA's from 0.00.0 to 4.04.0 and India (GPA's from 0.00.0 to 710.010.0) what is the probability that the student is from India?... 8As we know from statistics, given the mixture distribution and given the 9fact that his/her GPA is exactly 4.04.0, the probability that the student 10is American must be 1.01.0 11(i.e. zero probability that the student is from India)." 12Probabilistic logic program from 13https://github.com/davidenitti/DC/blob/master/examples/indian-gpa.pl 14*/ 15:- use_module(library(mcintyre)). 16 17:- if(current_predicate(use_rendering/1)). 18:- use_rendering(c3). 19:- endif. 20:- mc. 21:- begin_lpad. 22 23is_density_A:0.95;is_discrete_A:0.05. 24% the probability distribution of GPA scores for American students is 25% continuous with probability 0.95 and discrete with probability 0.05 26 27agpa(A) beta(A,8,2) :- is_density_A. 28% the GPA of American students follows a beta distribution if the 29% distribution is continuous 30 31american_gpa(G) finite(G,[4.0:0.85,0.0:0.15]) :- is_discrete_A. 32% the GPA of American students is 4.0 with probability 0.85 and 0.0 with 33% probability 0.15 if the 34% distribution is discrete 35american_gpa(A):- agpa(A0), A is A0*4.0. 36% the GPA of American students is obtained by rescaling the value of agpa 37% to the (0.0,4.0) interval 38is_density_I : 0.99; is_discrete_I:0.01. 39% the probability distribution of GPA scores for Indian students is 40% continuous with probability 0.99 and discrete with probability 0.01 41igpa(I) beta(I,5,5) :- is_density_I. 42% the GPA of Indian students follows a beta distribution if the 43% distribution is continuous 44indian_gpa(I) finite(I,[0.0:0.1,10.0:0.9]):- is_discrete_I. 45% the GPA of Indian students is 10.0 with probability 0.9 and 0.0 with 46% probability 0.1 if the 47% distribution is discrete 48indian_gpa(I) :- igpa(I0), I is I0*10.0. 49% the GPA of Indian students is obtained by rescaling the value of igpa 50% to the (0.0,4.0) interval 51nation(N) finite(N,[a:0.25,i:0.75]). 52% the nation is America with probability 0.25 and India with probability 0.75 53student_gpa(G):- nation(a),american_gpa(G). 54% the GPA of the student is given by american_gpa if the nation is America 55student_gpa(G) :- nation(i),indian_gpa(G). 56% the GPA of the student is given by indian_gpa if the nation is India 57 58:- end_lpad.

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`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*/