标题： 使用马尔可夫链蒙特卡罗方法的复杂模型随机输入采样 显示英文标题

标题： Random Input Sampling for Complex Models Using Markov Chain Monte Carlo

摘要： 许多随机过程可以被模拟为确定性模型的输出，该模型接受随机输入。 这种模型通常描述一个复杂的数学或物理随机系统，并且随机性被引入到模型的输入变量中。 当输出事件的统计特性已知时，这些输入变量必须以特定的方式选择，以便输出具有指定的统计特性。 由于输入随机变量的概率分布不是直接已知的，而是由输出随机变量的统计特性隐式决定的，因此对于经典的采样方法来说，这个问题通常是难以处理的。 基于马尔可夫链蒙特卡洛（MCMC）方法，我们提出了一种新的方法来通过修改标准的Metropolis-Hastings算法来采样此类模型的随机输入。 作为一个例子，我们考虑由随机微分方程（SDE）描述的系统，并演示如何使用我们的技术生成满足此SDE的随机过程的样本路径。 显示英文摘要

摘要： Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input variables have to be chosen in a specific way for the output to have the prescribed statistics. Because the probability distribution of the input random variables is not directly known but dictated implicitly by the statistics of the output random variables, this problem is usually intractable for classical sampling methods. Based on Markov Chain Monte Carlo we propose a novel method to sample random inputs to such models by introducing a modification to the standard Metropolis-Hastings algorithm. As an example we consider a system described by a stochastic differential equation (sde) and demonstrate how sample paths of a random process satisfying this sde can be generated with our technique.