Subsampling Sequential Monte Carlo for Static Bayesian Models

Our article shows how to carry out Bayesian inference by combining data subsampling with Sequential Monte Carlo (SMC). This takes advantage of the attractive properties of SMC for Bayesian computations with the ability of subsampling to tackle big data problems. SMC sequentially updates a cloud of particles through a sequence of densities, beginning with a density that is easy to sample from such as the prior and ending with the posterior density. 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 and 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 a great advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. First, a Hamiltonian Monte Carlo update makes distant moves for the model parameters. Second, a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate the usefulness of the methodology using two large datasets.