We present a variant of the sequential Monte Carlo sampler by incorporating the partial rejection control mechanism of Liu (2001). We show that the resulting algorithm can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler can reduce the variance of the incremental importance weights when compared with standard sequential Monte Carlo samplers, and provide a central limit theorem. Finally, the sampler is adapted for application under the challenging approximate Bayesian computation modelling framework.
Peters, G. W., Fan, Y., & Sisson, S. A. (2012). On sequential Monte Carlo, partial rejection control and approximate Bayesian computation. Statistics and Computing, 22(6), 1209-1222. https://doi.org/10.1007/s11222-012-9315-y