changeOfVarsDemo1d.m

%% Change of Variables Demo 1D
% x ~ U(-1,1), y=x^2, plot pdf of y
%%

% This file is from pmtk3.googlecode.com

xs = -1:0.1:1;
a = -1; b = 1;
%dist = UnifDist(a,b);
%px = exp(logprob(dist, xs));
px = 1/(b-a) * ones(1,length(xs));
fn = @(x) x.^2;
ys = fn(xs);

% analtyic
ppy = 1./(2*sqrt(ys));

% Monte Carlo
n=1000;
%samples = sample(dist, 1000);
samples = rand(1, 1000)*(b-a) + a; % sample from U(a,b)
samples2 = fn(samples);
%[f, xi] = ksdensity(samples2);
[h,bins] = hist(samples2,20);
h = normalize(h);

figure(2);clf
nr = 1; nc = 3;
subplot(nr,nc,1); plot(xs, px, '-');
subplot(nr,nc,2); plot(ys, ppy, '-');
subplot(nr,nc,3);  bar(bins,h);

printPmtkFigure('changeOfVars');