Design and analysis of efficient quasi-Monte Carlo sampling methods

在大量的科学学科中，随机模型被用来表示系统，必须对某些感兴趣的量进行评估。例如，生产经理可能需要根据预期成本比较不同的库存策略，假设供应和需求都受到某种形式的随机性的影响，或者电信网络设计师可能希望根据处理大量随机信息流的能力来比较不同的设计，而不会导致损失或减速。蒙特卡罗方法可以用来回答复杂系统的性质问题，其特征是多个随机相互作用的组件。该方法使用随机抽样，以“模拟”所研究系统的可能场景，并对每个场景评估感兴趣的数量的相应值。通过多次重复该过程，创建了该量的可能值的样本，然后可以将其用于推断，例如，样本平均值可以用作感兴趣的量的估计器。

In a large number of scientific disciplines, stochastic models are used to represent systems for which certain quantities of interest must be evaluated. For example, a production manager might need to compare different inventory policies in terms of their expected cost, assuming that supply and demand are both subjected to some form of randomness, or a telecommunication network designer might want to compare different designs based on their ability to handle large stochastic flows of information without incurring losses or slow-downs. The Monte Carlo method can be used to answer questions of that nature for complex systems which feature several random interacting components. This method uses random sampling in order to "simulate" possible scenarios for the system under study, and for each, the corresponding value of the quantity of interest is evaluated. By repeating this process several times, a sample of possible values for this quantity is created, which can then be used for inference, e.g., the sample mean can be used as an estimator for the quantity of interest.