  We present results on the estimation and evaluation of success probabilities
for ordinal optimisation over uncountable sets (such as subsets of
$\mathbb{R}^{d}$). Our formulation invokes an assumption of a Gaussian copula
model, and we show that the success probability can be equivalently computed by
assuming a special case of additive noise. We formally prove a lower bound on
the success probability under the Gaussian copula model, and numerical
experiments demonstrate that the lower bound yields a reasonable approximation
to the actual success probability. Lastly, we showcase the utility of our
results by guaranteeing high success probabilities with ordinal optimisation.
