A standard way to move particles in a SMC sampler is to apply several steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste-free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decreases across iterations (as in tempering or rare event problems).

翻译：在 SMC 取样器中移动粒子的标准方式是应用一个 MCMC (Markov 链条 Monte Carlo) 的几步 。 不幸的是, 不清楚需要执行多少步骤才能达到最佳性能。 此外, 中间步骤的输出被丢弃, 从而以某种方式浪费。 我们提出一种新的无废弃物的 SMC 算法, 将所有这些中间MC 步骤的输出都用作粒子。 我们确定它的输出是一致的, 并且不那么正常 。 我们使用无症状差异的表达法来发展如何在实践中实施算法的各种洞察。 我们特别开发了一种方法, 从算法的单行算法中估算任何粒子估计的无症状差异。 我们通过一系列数字实例, 实验性地显示无废弃物的 SMC 往往超越标准 SMC 采样器的输出, 特别是当考虑的MC 内核的混合过程在迭代之间减少( 如调或罕见事件问题 ) 的情况下 。