Optimal budget allocation for stochastic simulation with importance sampling: Exploration vs. replication

This article investigates a budget allocation problem for optimally running stochastic simulation models with importance sampling in computer experiments. In particular, we consider a two-level (or nested) simulation to estimate the expectation of the simulation output, where the first-level draws random input samples and the second-level obtains the output given the input from the first-level. The two-level simulation faces the trade-off in allocating the computational budgets: exploring more inputs (exploration) or exploiting the stochastic response surface at a sampled point in more detail (replication). We study an appropriate computational budget allocation strategy that strikes a balance between exploration and replication to minimize the variance of the estimator when importance sampling is employed at the first-level simulation. Our analysis suggests that exploration can be beneficial than replication in many practical situations. We also conduct numerical experiments in a wide range of settings and wind turbine case study to investigate the trade-off.