Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC$^2$) are two methods that use an unbiased estimate of the log-likelihood obtained from a particle filter (PF) to evaluate the target distribution. P-MCMC constructs a single Markov chain which is sequential by nature so cannot be readily parallelized using Distributed Memory (DM) architectures. This is in contrast to SMC$^2$ which includes processes, such as importance sampling, that are described as \textit{embarrassingly parallel}. However, difficulties arise when attempting to parallelize resampling. None-the-less, the choice of backward kernel, recycling scheme and compatibility with DM architectures makes SMC$^2$ an attractive option when compared with p-MCMC. In this paper, we present an SMC$^2$ framework that includes the following features: an optimal (in terms of time complexity) $\mathcal{O}(\log_2N)$ parallelization for DM architectures, an approximately optimal (in terms of accuracy) backward kernel, and an efficient recycling scheme. On a cluster of $128$ DM processors, the results on a biomedical application show that SMC$^2$ achieves up to a $70\times$ speed-up vs its sequential implementation. It is also more accurate and roughly $54\times$ faster than p-MCMC. A GitHub link is given which provides access to the code.

翻译：使用贝叶斯推断校准统计模型通常需要既准确又及时的参数估计。粒子马尔可夫链蒙特卡洛（p-MCMC）和序贯蒙特卡洛平方（SMC$^2$）是两种利用粒子滤波器（PF）获得的对数似然无偏估计来评估目标分布的方法。P-MCMC构建单一马尔可夫链，其本质上是序贯的，因此不易利用分布式内存（DM）架构进行并行化。这与SMC$^2$形成对比，后者包含诸如重要性采样等被称为“平凡并行”的过程。然而，在尝试并行化重采样时会出现困难。尽管如此，向后核的选择、回收方案以及与DM架构的兼容性使得SMC$^2$相比p-MCMC成为一个有吸引力的选择。在本文中，我们提出了一种SMC$^2$框架，该框架包含以下特性：一种（在时间复杂度上）最优的 $\mathcal{O}(\log_2N)$ DM架构并行化方法，一种（在精度上）近似最优的向后核，以及一种高效的回收方案。在一个由$128$个DM处理器组成的集群上，针对生物医学应用的结果表明，与顺序实现相比，SMC$^2$可实现高达$70$倍的加速。与p-MCMC相比，它也更准确，且速度大约快$54$倍。文中提供了GitHub链接，用于访问相关代码。