If cov(f(x1),f(x2)) is positive, does that mean f is close to symmetric along x1 and x2? I am struggling to put this into understandable terms.
Edit:
The context is equation 6 in this paper: http://salserver.org.aalto.fi/vanhat_sivut/Opinnot/Mat-2.4108/pdf-files/emat08.pdf if cov(f(x1), f(x2)) is positive, the sampling error is not reduced by the hypercube sampling technique. I would like to "translate" this to a rule of thumb as to whether lhs sampling will be useful based on the geometry of f.