  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.
