Iterated sampling importance resampling (i-SIR) is a Markov chain Monte Carlo (MCMC) algorithm which is based on $N$ independent proposals. As $N$ grows, its samples become nearly independent, but with an increased computational cost. We discuss a method which finds an approximately optimal number of proposals $N$ in terms of the asymptotic efficiency. The optimal $N$ depends on both the mixing properties of the i-SIR chain and the (parallel) computing costs. Our method for finding an appropriate $N$ is based on an approximate asymptotic variance of the i-SIR, which has similar properties as the i-SIR asymptotic variance, and a generalised i-SIR transition having fractional `number of proposals.' These lead to an adaptive i-SIR algorithm, which tunes the number of proposals automatically during sampling. Our experiments demonstrate that our approximate efficiency and the adaptive i-SIR algorithm have promising empirical behaviour. We also present new theoretical results regarding the i-SIR, such as the convexity of asymptotic variance in the number of proposals, which can be of independent interest.

翻译：迭代采样重要性重采样（i-SIR）是一种基于$N$个独立提议的马尔可夫链蒙特卡洛（MCMC）算法。随着$N$增大，其样本趋于近似独立，但计算成本随之增加。本文讨论了一种根据渐近效率近似确定最优提议数量$N$的方法。最优$N$取决于i-SIR链的混合特性与（并行）计算成本。我们确定合适$N$的方法基于i-SIR的近似渐近方差——该方差具有与i-SIR渐近方差相似的性质，以及具有分数“提议数量”的广义i-SIR转移核。这些推导引出了自适应i-SIR算法，该算法能在采样过程中自动调整提议数量。实验表明，我们的近似效率度量与自适应i-SIR算法均展现出良好的实证性能。本文还提出了关于i-SIR的新理论结果，例如渐近方差在提议数量上的凸性，这些结果可能具有独立的理论价值。