By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, the tool for the evaluation of Bayesian inference problems that yield non-standard posterior distributions. In recent years, however, it has become apparent that Sequential Monte Carlo (SMC) samplers have the potential to outperform MCMC in several ways. SMC samplers are better suited to highly parallel computing architectures and also feature various tuning parameters that are not available to MCMC. One such parameter – the ‘L-kernel’ – is a user-defined probability distribution that can be used to influence the efficiency of the sampler. In the current paper, the authors explain how to derive an expression for the L-kernel that minimises the variance of the estimates realised by an SMC sampler. Various approximation methods are then proposed to aid the implementation of the proposed L-kernel. The improved performance of the resulting algorithm is demonstrated in multiple scenarios. For the examples shown in the current paper, the use of an approximately optimal L-kernel has reduced the variance of the SMC estimates by up to 99 % while also reducing the number of times that resampling was required by between 65% and 70%. Python code and code tests accompanying this manuscript are available through the Github repository https://github.com/plgreenLIRU/SMC_approx_optL.

通过促进从任意概率分布中生成样本，马尔可夫链蒙特卡洛（MCMC）可以说是用于评估产生非标准后验分布的贝叶斯推理问题的工具。但是，近年来，顺序蒙特卡洛（SMC）采样器具有在几种方面胜过MCMC的潜力，这一点已变得显而易见。SMC采样器更适合高度并行的计算体系结构，并且具有MCMC无法使用的各种调整参数。其中一个参数-“ L-kernel”（L内核）是用户定义的概率分布，可用于影响采样器的效率。在当前的论文中，作者解释了如何导出L核的表达式，该表达式使SMC采样器实现的估计值的方差最小。然后提出了各种近似方法来帮助实现所提出的L核。在多种情况下证明了所得算法的改进性能。对于当前论文中显示的示例，使用近似最佳的L核已将SMC估计值的方差减少了多达99％，同时还将需要重采样的次数减少了65％至70％。可通过Github存储库https://github.com/plgreenLIRU/SMC_approx_optL获得该手稿随附的Python代码和代码测试。