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必须对其特定的兴趣量进行评估的系统。例如，假设供应和需求都受到某种形式的随机性的影响，生产经理可能需要在预期成本方面比较不同的库存策略，或者电信网络设计人员可能希望比较不同的设计，基于它们处理大型随机信息流的能力，而不会招致损失或速度减慢。蒙特卡罗方法可用于回答具有多个随机相互作用组件的复杂系统的性质问题。这种方法使用随机抽样，以便为所研究的系统“模拟”可能的情景，并对每一种情景的兴趣量的相应数值进行评估。通过多次重复这一过程，创建了该数量的可能平均值的样本，然后可以使用该样本平均值进行推断，例如，样本平均值可以用作感兴趣数量的估计器。

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.