Sequential Monte Carlo (SMC) methods are powerful alternatives to standard Markov chain Monte Carlo (MCMC) for sampling from the posterior of complex static Bayesian models. SMC is naturally adaptive, parallelisable and capable of dealing with complex and multimodal targets. However, SMC is generally seen as more difficult to implement than MCMC. R packages like RcppSMC could help to make these methods more accessible.

An estimate of the marginal likelihood (normalising constant or evidence) can be obtained as a by-product of SMC (see e.g. Del Moral et al (2006)). Adjusting the current RcppSMC package to allow for estimation of the marginal likelihood would be useful for model choice and for exact-approximate methods such as particle MCMC (Andrieu et al., 2010).

There is a plethora of choices for advanced SMC implementations since this is an active area of research. Some of the possibilities have been described in more detail in the timeline below.