  We study the success probability for a variant of the secretary problem, with
noisy observations and multiple offline selection. Our formulation emulates,
and is motivated by, problems involving noisy selection arising in the
disciplines of stochastic simulation and simulation-based optimisation. In
addition, we employ the philosophy of ordinal optimisation - involving an
ordinal selection rule, and a percentile notion of goal softening for the
success probability. As a result, it is shown that the success probability only
depends on the underlying copula of the problem. Other general properties for
the success probability are also presented. Specialising to the case of
Gaussian copulas, we also derive an analytic lower bound for the success
probability, which may then be inverted to find sufficiently large sample sizes
that guarantee a high success probability arbitrarily close to one.
