论文标题
随机重量顺序蒙特卡洛法的收敛性
Convergence of random-weight sequential Monte Carlo methods
论文作者
论文摘要
我们研究了顺序蒙特卡洛法的性质，其中出现在算法中的粒子的重量是由正，公正的估计量估算的。我们提出了广泛的可融合结果，包括中心限制定理，我们讨论了它们与统计物理应用的相关性。使用这些结果，我们表明重采样步骤减少了权重随机性对估计量渐近方差的影响。此外，我们探讨了顺序蒙特卡洛法的收敛范围，重点是几乎确定的收敛。我们构建了一个示例算法，我们可以在概率中证明会聚，但是即使在非随机重量的情况下，几乎肯定不会收敛。
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central limit theorem, and we discuss their relevance for applications in statistical physics. Using these results, we show that the resampling step reduces the impact of the randomness of the weights on the asymptotic variance of the estimator. In addition, we explore the limits of convergence of the sequential Monte Carlo method, with a focus on almost sure convergence. We construct an example algorithm where we can prove convergence in probability, but which does not converge almost surely, even in the non-random-weight case.
