I am doing a simulation test to check that my method should be working as expected. I would be defining by three variables X, Y, Z using the dirichlet distribution for X, and a gaussian for Z and Y. The goal would be to define and predict Y = theta f(X)+g(Z)+N_y, where X=N_x, Z=N_x+X and to plot a graph where the x-axis represents theta and Y the rejection rate. Testing for conditinal independence between E[Y|X,Z]=E[Y|Z]. This should end with being able to see how as theta increases the rate of rejection would rise.