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Convergence of sequential quasi-Monte Carlo smoothing algorithms

机译:序贯拟蒙特卡罗平滑算法的收敛性

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摘要

[17] recently introduced Sequential quasi-Monte Carlo (SQMC) algorithms as an efficient way to perform filtering in state-space models. The basic idea is to replace random variables with low-discrepancy point sets, so as to obtain faster convergence than with standard particle filtering. [17] describe briefly several ways to extend SQMC to smoothing, but do not provide supporting theory for this extension. We discuss more thoroughly how smoothing may be performed within SQMC, and derive convergence results for the so-obtained smoothing algorithms. We consider in particular SQMC equivalents of forward smoothing and forward filtering backward sampling, which are the most well-known smoothing techniques.As a preliminary step, we provide a generalization of the classical result of [22] on the transformation of QMC point sets into low discrepancy point sets with respect to non uniform distributions. As a corollary of the latter, we note that we can slightly weaken the assumptions to prove the consistency of SQMC.
机译:[17]最近介绍了序列准蒙特卡罗(SQMC)算法,作为在状态空间模型中执行过滤的有效方法。基本思想是用低差异点集代替随机变量,从而获得比标准粒子滤波更快的收敛速度。 [17]简要描述了几种将SQMC扩展到平滑的方法,但是没有为这种扩展提供支持理论。我们将更全面地讨论如何在SQMC中执行平滑操作,并得出如此获得的平滑算法的收敛结果。我们特别考虑前向平滑和前向滤波后向采样的SQMC等效项,它们是最著名的平滑技术。作为第一步,我们将[22]的经典结果推广到了QMC点集到关于非均匀分布的低差异点集。作为后者的推论,我们注意到我们可以稍微削弱假设以证明SQMC的一致性。

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