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Multilevel rejection sampling for approximate Bayesian computation

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  • Warne, David J.
  • Baker, Ruth E.
  • Simpson, Matthew J.

Abstract

Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate Bayesian computation can be effective techniques for sampling posterior distributions in an approximate Bayesian computation setting. However, without careful consideration of convergence criteria and selection of proposal kernels, such methods can lead to very biased inference or computationally inefficient sampling. In contrast, rejection sampling for approximate Bayesian computation, despite being computationally intensive, results in independent, identically distributed samples from the approximated posterior. An alternative method is proposed for the acceleration of likelihood-free Bayesian inference that applies multilevel Monte Carlo variance reduction techniques directly to rejection sampling. The resulting method retains the accuracy advantages of rejection sampling while significantly improving the computational efficiency.

Suggested Citation

  • Warne, David J. & Baker, Ruth E. & Simpson, Matthew J., 2018. "Multilevel rejection sampling for approximate Bayesian computation," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 71-86.
    • Handle: RePEc:eee:csdana:v:124:y:2018:i:c:p:71-86
    DOI: 10.1016/j.csda.2018.02.009
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    References listed on IDEAS

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    Cited by:

    1. Zhu, Chuanqi & Tian, Wei & Yin, Baoquan & Li, Zhanyong & Shi, Jiaxin, 2020. "Uncertainty calibration of building energy models by combining approximate Bayesian computation and machine learning algorithms," Applied Energy, Elsevier, vol. 268(C).

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