The Bayesian posterior distribution can only be evaluated up-to a constant of proportionality, which makes simulation and consistent estimation challenging. Classical consistent Bayesian methods such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) have unbounded time complexity requirements. We develop a fully parallel sequential Monte Carlo (pSMC) method which provably delivers parallel strong scaling, i.e. the time complexity (and per-node memory) remains bounded if the number of asynchronous processes is allowed to grow. More precisely, the pSMC has a theoretical convergence rate of Mean Square Error (MSE)$ = O(1/NP)$, where $N$ denotes the number of communicating samples in each processor and $P$ denotes the number of processors. In particular, for suitably-large problem-dependent $N$, as $P \rightarrow \infty$ the method converges to infinitesimal accuracy MSE$=O(\varepsilon^2)$ with a fixed finite time-complexity Cost$=O(1)$ and with no efficiency leakage, i.e. computational complexity Cost$=O(\varepsilon^{-2})$. A number of Bayesian inference problems are taken into consideration to compare the pSMC and MCMC methods.

翻译：贝叶斯后验分布仅能计算到比例常数，这使得模拟与一致性估计具有挑战性。经典的一致性贝叶斯方法，如序贯蒙特卡洛（SMC）和马尔可夫链蒙特卡洛（MCMC），具有无界的时间复杂度要求。我们开发了一种完全并行的序贯蒙特卡洛（pSMC）方法，该方法可证明实现并行强扩展，即若允许异步进程数量增长，时间复杂度（及每节点内存）保持有界。更精确地说，pSMC的理论收敛速度为均方误差（MSE）$ = O(1/NP)$，其中$N$表示每个处理器中通信样本的数量，$P$表示处理器数量。特别地，对于充分大的问题相关$N$，当$P \rightarrow \infty$时，该方法以固定的有限时间复杂度Cost$=O(1)$收敛到无穷小精度MSE$=O(\varepsilon^2)$，且无效率损失，即计算复杂度Cost$=O(\varepsilon^{-2})$。本文考虑了若干贝叶斯推断问题以比较pSMC与MCMC方法。