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

An $\mathcal{O}(\log_2N)$ SMC$^2$ Algorithm on Distributed Memory with an Approx. Optimal L-Kernel