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On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

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Abstract

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.

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Authors and Affiliations

  1. CSIRO Sydney, Locked Bag 17, North Ryde, NSW, 1670, Australia

    G. W. Peters

  2. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    G. W. Peters, Y. Fan & S. A. Sisson

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  1. G. W. Peters
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  2. Y. Fan
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  3. S. A. Sisson
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Correspondence to S. A. Sisson.

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Peters, G.W., Fan, Y. & Sisson, S.A. On sequential Monte Carlo, partial rejection control and approximate Bayesian computation. Stat Comput 22, 1209–1222 (2012). https://doi.org/10.1007/s11222-012-9315-y

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  • DOI: https://doi.org/10.1007/s11222-012-9315-y

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