Properties of marginal sequential Monte Carlo methods

We provide a framework which admits a number of “marginal” sequential Monte Carlo (SMC) algorithms as particular cases — including the marginal particle filter (Klaas et al., 2005), the independent particle filter (Lin et al., 2005) and linear-cost Approximate Bayesian Computation SMC (Sisson et al., 2007). We provide conditions under which such algorithms obey laws of large numbers and central limit theorems and provide some further asymptotic characterizations. Finally, it is shown that the asymptotic variance of a class of estimators associated with certain marginal SMC algorithms is never greater than that of the estimators provided by a standard SMC algorithm using the same proposal distributions.