Optimal budget allocation for stochastic simulation with importance sampling: Exploration vs. replication
研究了两层随机模拟中计算预算如何在探索更多输入与复制已有输入之间分配，以最小化估计量方差，发现探索通常比复制更有效。
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.