  We propose nested sequential Monte Carlo (NSMC), a methodology to sample from
sequences of probability distributions, even where the random variables are
high-dimensional. NSMC generalises the SMC framework by requiring only
approximate, properly weighted, samples from the SMC proposal distribution,
while still resulting in a correct SMC algorithm. Furthermore, NSMC can in
itself be used to produce such properly weighted samples. Consequently, one
NSMC sampler can be used to construct an efficient high-dimensional proposal
distribution for another NSMC sampler, and this nesting of the algorithm can be
done to an arbitrary degree. This allows us to consider complex and
high-dimensional models using SMC. We show results that motivate the efficacy
of our approach on several filtering problems with dimensions in the order of
100 to 1 000.
