% Example 4.1 part 2 from the paper
% SSVS on a small synthetic dataset with a "strong proxy".
n = 60;
p = 5;
a = zeros(n,1);
b = eye(n);

X1 = mvnrnd(a,b)';
X2 = mvnrnd(a,b)';
X4 = mvnrnd(a,b)';
X5 = mvnrnd(a,b)';

% Introduce a modified X3 that is a "strong proxy" for X5
Z = mvnrnd(a,b)';
X3 = X5 + 0.15 * Z;

% Noise
s = 2.5;
e = mvnrnd(a,s*s*b)';

Y = X4 + 1.2 * X5 + e;
X = [X1,X2,X3,X4,X5];

samples = ssvs(X,Y,5000,[1,5]);
counts = count(samples)