  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, in: Proceedings of Uncertainty in Artificial
Intelligence, pp. 308--315], , the independent particle filter [Lin et al.,
2005, Journal of the American Statistical Association 100, pp. 1412--1421] and
linear-cost Approximate Bayesian Computation SMC [Sisson et al., 2007,
Proceedings of the National Academy of Sciences (USA) 104, pp. 1760--1765.]. 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.
