/* Posterior estimation in Bayesian models. We are trying to estimate the true value of a Gaussian distributed random variable, given some observed data. The variance is known (2) and we suppose that the mean has a Gaussian distribution with mean 1 and variance 5. We take different measurement (e.g. at different times), indexed with an integer. Given that we observe 9 and 8 at indexes 1 and 2, how does the distribution of the random variable (value at index 0) changes with respect to the case of no observations? From http://www.robots.ox.ac.uk/~fwood/anglican/examples/viewer/?worksheet=gaussian-posteriors */ :- use_module(library(mcintyre)). :- use_module(library(cplint_r)). :- mc. :- begin_lpad. value(I,X) :- mean(M), value(I,M,X). % at time I we see X sampled from a Gaussian with mean M and variamce 2.0 mean(M): gaussian(M,1.0, 5.0). % Gaussian distribution of the mean of the Gaussian of the variable value(_,M,X): gaussian(X,M, 2.0). % Gaussian distribution of the variable :- end_lpad. hist_uncond(Samples,NBins):- mc_sample_arg(value(0,X),Samples,X,L0), histogram_r(L0,NBins). % plot an histogram of the density of the random variable before any % observations by taking Samples samples and by dividing the domain % in NBins bins dens_lw(Samples):- mc_sample_arg(value(0,Y),Samples,Y,L0), mc_lw_sample_arg(value(0,X),(value(1,9),value(2,8)),Samples,X,L), densities_r(L0,L). % plot the densities of the random variable before and after % observing 9 and 8 by taking Samples samples. /** ?- dens_lw(1000). % plot the densities of the random variable before and after % observing 9 and 8 ?- hist_uncond(10000,40). % plot an histogram of the density of the random variable before any % observations ?- mc_lw_expectation(value(0,X),(value(1,9),value(2,8)),1000,X,E). % E = 7.166960047178755 ?- mc_expectation(value(0,X),10000,X,E). % E = 0.9698875384639362. */