  In nested simulation literature, a common assumption is that the experimenter
can choose the number of outer scenarios to sample. This paper considers the
case when the experimenter is given a fixed set of outer scenarios from an
external entity. We propose a nested simulation experiment design that pools
inner replications from one scenario to estimate another scenario's conditional
mean via the likelihood ratio method. Given the outer scenarios, we decide how
many inner replications to run at each outer scenario as well as how to pool
the inner replications by solving a bi-level optimization problem that
minimizes the total simulation effort. We provide asymptotic analyses on the
convergence rates of the performance measure estimators computed from the
optimized experiment design. Under some assumptions, the optimized design
achieves $\cO(\Gamma^{-1})$ mean squared error of the estimators given
simulation budget $\Gamma$. Numerical experiments demonstrate that our design
outperforms a state-of-the-art design that pools replications via regression.
