  We investigate sampling laws for particle algorithms and the influence of
these laws on the efficiency of particle approximations of marginal likelihoods
in hidden Markov models. Among a broad class of candidates we characterize the
essentially unique family of particle system transition kernels which is
optimal with respect to an asymptotic-in-time variance growth rate criterion.
The sampling structure of the algorithm defined by these optimal transitions
turns out to be only subtly different from standard algorithms and yet the
fluctuation properties of the estimates it provides can be dramatically
different. The structure of the optimal transition suggests a new class of
algorithms, which we term "twisted" particle filters and which we validate with
asymptotic analysis of a more traditional nature, in the regime where the
number of particles tends to infinity.
