Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in statistics and related fields; e.g. for inference in non-linear non-Gaussian state space models, and in complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which crucially impact their performance. We introduce here a class of controlled sequential Monte Carlo algorithms, where the proposal distributions are determined by approximating the solution to an associated optimal control problem using an iterative scheme. This method builds upon a number of existing algorithms in econometrics, physics, and statistics for inference in state space models, and generalizes these methods so as to accommodate complex static models. We provide a theoretical analysis concerning the fluctuation and stability of this methodology that also provides insight into the properties of related algorithms. We demonstrate significant gains over state-of-the-art methods at a fixed computational complexity on a variety of applications.

中文翻译：

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受控顺序蒙特卡罗

顺序蒙特卡罗方法，也称为粒子方法，是一组流行的用于逼近高维概率分布及其归一化常数的技术。这些方法在统计学和相关领域有很多应用。例如，用于非线性非高斯状态空间模型和复杂静态模型的推理。像许多蒙特卡洛采样方案一样，它们依赖于对它们的性能产生关键影响的提议分布。我们在此介绍一类受控顺序蒙特卡罗算法，其中提议分布是通过使用迭代方案逼近相关最优控制问题的解决方案来确定的。该方法建立在计量经济学、物理学和统计学中的许多现有算法之上，用于状态空间模型的推理，并概括这些方法以适应复杂的静态模型。我们提供了关于这种方法的波动和稳定性的理论分析，也提供了对相关算法特性的深入了解。我们在各种应用程序中以固定的计算复杂度展示了优于最先进方法的显着收益。