  A key limitation of sampling algorithms for approximate inference is that it
is difficult to quantify their approximation error. Widely used sampling
schemes, such as sequential importance sampling with resampling and
Metropolis-Hastings, produce output samples drawn from a distribution that may
be far from the target posterior distribution. This paper shows how to
upper-bound the symmetric KL divergence between the output distribution of a
broad class of sequential Monte Carlo (SMC) samplers and their target posterior
distributions, subject to assumptions about the accuracy of a separate
gold-standard sampler. The proposed method applies to samplers that combine
multiple particles, multinomial resampling, and rejuvenation kernels. The
experiments show the technique being used to estimate bounds on the divergence
of SMC samplers for posterior inference in a Bayesian linear regression model
and a Dirichlet process mixture model.
