1/* 2Factory producing widgets. 3Consider a factory with two machines a and b. Each machine produces a widget 4with a continuous feature. A widget is produced by machine a with probability 50.7 and by machine b with probability b. 6If the widget is produced by machine a, the feature is distributed as a 7Gaussian with mean 2.0 and variance 1.0. 8If the widget is produced by machine b, the feature is distributed as a 9Gaussian with mean 3.0 and variance 1.0. 10The widget then is processed by a third machine that adds a random quantity to 11the feature distributed as a Gaussian with mean 0.5 and variance 0.1. 12What is the distribution of the feature? 13What is the distribution of the feature given that the widget was procuded 14by machine a? 15What is the distribution of the feature given that the third machine added a 16quantity greater than 0.2? 17What is the distribution of the feature given that the third machine added 18a quantity of 2.0? 19Adapted from 20Islam, Muhammad Asiful, C. R. Ramakrishnan, and I. V. Ramakrishnan. 21"Inference in probabilistic logic programs with continuous random variables." 22Theory and Practice of Logic Programming 12.4-5 (2012): 505-523. 23http://arxiv.org/pdf/1112.2681v3.pdf 24*/ 25:- use_module(library(mcintyre)). 26:- use_module(library(clpr)). 27 28:- if(current_predicate(use_rendering/1)). 29:- use_rendering(c3). 30:- endif. 31:- mc. 32:- begin_lpad. 33 34widget(X) :- 35 machine(M), 36 st(M,Z), 37 pt(Y), 38 {X =:= Y + Z}. 39 40machine(a):0.3;machine(b):0.7. 41 42st(a,X) gaussian(X,2.0, 1.0). 43 44st(b,X) gaussian(X,3.0, 1.0). 45 46pt(X) gaussian(X,0.5, 0.1). 47 48 49:- end_lpad. 50 51hist_uncond(Samples,NBins,Chart):- 52 mc_sample_arg(widget(X),Samples,X,L0), 53 histogram(L0,Chart,[nbins(NBins)]). 54% What is the distribution of the feature? 55 56hist_rej_macha(Samples,NBins,Chart):- 57 mc_rejection_sample_arg(widget(X),machine(a),Samples,X,L0), 58 histogram(L0,Chart,[nbins(NBins)]). 59% What is the distribution of the feature given that the widget was procuded 60% by machine a, computed by taking Samples samples with rejection sampling and 61% drawing a histogram with NBins bins? 62 63hist_mh_macha(Samples,Lag,NBins,Chart):- 64 mc_mh_sample_arg(widget(X),machine(a),Samples,X,L0,[lag(Lag)]), 65 histogram(L0,Chart,[nbins(NBins)]). 66% What is the distribution of the feature given that the widget was procuded 67% by machine a, computed by taking Samples samples with Metropolis-Hastings 68% (lag=Lag) and drawing a histogram with NBins bins? 69 70hist_rej_dis(Samples,NBins,Chart):- 71 mc_rejection_sample_arg(widget(X),(pt(Y),Y>0.2),Samples,X,L0), 72 histogram(L0,Chart,[nbins(NBins)]). 73% What is the distribution of the feature given that the third machine added a 74% quantity greater than 0.2, computed by taking Samples samples with rejection 75% sampling and 76% drawing a histogram with NBins bins? 77 78hist_mh_dis(Samples,Lag,NBins,Chart):- 79 mc_mh_sample_arg(widget(X),(pt(Y),Y>0.2),Samples,X,L0,[lag(Lag)]), 80 histogram(L0,Chart,[nbins(NBins)]). 81% What is the distribution of the feature given that the third machine added a 82% quantity greater than 0.2, computed by taking Samples samples with 83% Metropolis-Hastings and 84% drawing a histogram with NBins bins? 85 86hist_lw(Samples,NBins,Chart):- 87 mc_sample_arg(widget(Y),Samples,Y,L0), 88 mc_lw_sample_arg(widget(X),pt(2.0),Samples,X,L), 89 densities(L0,L,Chart,[nbins(NBins)]). 90% What is the distribution of the feature given that the third machine added 91% a quantity of 2.0, computed by taking Samples samples with likelihood weighting 92% and drawing a density with NBins bins?

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`hist_lw(1000,40,G)`

. % What is the distribution of the feature given that the third machine added % a quantity of 2.0, computed by taking 1000 samples with likelihood weighting % and drawing a density with 40 bins??-

`hist_uncond(10000,40,G)`

. % What is the distribution of the feature??-

`hist_rej_macha(10000,40,G)`

. % What is the distribution of the feature given that the widget was procuded % by machine a, computed by taking 10000 samples with rejection sampling and % drawing a histogram with 40 bins??-

`hist_mh_macha(10000,2,40,G)`

. % What is the distribution of the feature given that the widget was procuded % by machine a, computed by taking 10000 samples with Metropolis-Hastings % (lag=Lag) and drawing a histogram with 40 bins??-

`hist_rej_dis(10000,40,G)`

. % What is the distribution of the feature given that the third machine added a % quantity greater than 0.2, computed by taking 10000 samples with rejection % sampling and % drawing a histogram with 40 bins??-

`hist_mh_dis(10000,2,40,G)`

. % What is the distribution of the feature given that the third machine added a % quantity greater than 0.2, computed by taking 10000 samples with % Metropolis-Hastings and % drawing a histogram with 40 bins?*/