We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of distributions, and then specialise our results to tempering sequences. We use our results to derive the complexity of SMC samplers with respect to the parameters of the problem, such as $T$, the number of target distributions, in the general case, or $d$, the dimension of the ambient space, in the tempering case. We use these bounds to derive practical recommendations for the implementation of SMC samplers for end users.

翻译：我们建立了标准和免浪费SMC采样器误差的有限样本界。我们的结果涵盖了对目标分布的期望和归一化常数的估计。我们首先考虑任意序列的分布，然后专门针对温度序列令我们的结果具体化。我们利用这些结果推导出SMC采样器相对于问题参数（如一般情况下目标分布的个数$T$，或温度情况下环境空间的维度$d$）的复杂性。我们利用这些界为终端用户推导出关于SMC采样器实现的实用建议。