标题： 大偏差的数值方面 显示英文标题

标题： Numerical Aspects of Large Deviations

摘要： 提供了关于数值大偏差采样的介绍。 首先，解释了使用已知分布的直接偏置方法。 作为一个简单例子，文中自始至终使用了伯努利实验。 接下来，介绍了马尔可夫链蒙特卡洛（MCMC）模拟。 特别是解释了Metropolis-Hastings算法。 作为MCMC的第一个实现，展示了普通伯努利模型的采样。 接下来，对于同一个模型使用了指数偏置，这允许获取可测量量分布的尾部。 这种方法被推广到状态为$U(0,1)$随机条目的MCMC模拟中。 这使得可以使用指数或其他偏置来访问相当任意随机过程的大偏差特性。 最后，讨论了一些用于研究更复杂模型的近期研究应用。 显示英文摘要

摘要： An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli experiment is used throughout the text. Next, Markov chain Monte Carlo (MCMC) simulations are introduced. In particular, the Metropolis-Hastings algorithm is explained. As first implementation of MCMC, sampling of the plain Bernoulli model is shown. Next, an exponential bias is used for the same model, which allows one to obtain the tails of the distribution of a measurable quantity. This approach is generalized to MCMC simulations, where the states are vectors of $U(0,1)$ random entries. This allows one to use the exponential or any other bias to access the large-deviation properties of rather arbitrary random processes. Finally, some recent research applications to study more complex models are discussed.