  We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference
in large data problems by data subsampling. SMC sequentially updates a cloud of
particles through a sequence of distributions, beginning with a distribution
that is easy to sample from such as the prior and ending with the posterior
distribution. Each update of the particle cloud consists of three steps:
reweighting, resampling, and moving. In the move step, each particle is moved
using a Markov kernel; this is typically the most computationally expensive
part, particularly when the dataset is large. It is crucial to have an
efficient move step to ensure particle diversity. Our article makes two
important contributions. First, in order to speed up the SMC computation, we
use an approximately unbiased and efficient annealed likelihood estimator based
on data subsampling. The subsampling approach is more memory efficient than the
corresponding full data SMC, which is an advantage for parallel computation.
Second, we use a Metropolis within Gibbs kernel with two conditional updates. A
Hamiltonian Monte Carlo update makes distant moves for the model parameters,
and a block pseudo-marginal proposal is used for the particles corresponding to
the auxiliary variables for the data subsampling. We demonstrate both the
usefulness and limitations of the methodology for estimating four generalized
linear models and a generalized additive model with large datasets.
