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Choosing summary statistics by least angle regression for approximate Bayesian computation

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  • Muhammad Faisal
  • Andreas Futschik
  • Ijaz Hussain
  • Mitwali Abd-el.Moemen

Abstract

Bayesian statistical inference relies on the posterior distribution. Depending on the model, the posterior can be more or less difficult to derive. In recent years, there has been a lot of interest in complex settings where the likelihood is analytically intractable. In such situations, approximate Bayesian computation (ABC) provides an attractive way of carrying out Bayesian inference. For obtaining reliable posterior estimates however, it is important to keep the approximation errors small in ABC. The choice of an appropriate set of summary statistics plays a crucial role in this effort. Here, we report the development of a new algorithm that is based on least angle regression for choosing summary statistics. In two population genetic examples, the performance of the new algorithm is better than a previously proposed approach that uses partial least squares.

Suggested Citation

  • Muhammad Faisal & Andreas Futschik & Ijaz Hussain & Mitwali Abd-el.Moemen, 2016. "Choosing summary statistics by least angle regression for approximate Bayesian computation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2191-2202, September.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:12:p:2191-2202
    DOI: 10.1080/02664763.2015.1134447
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    References listed on IDEAS

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    1. Muhammad Faisal & Andreas Futschik & Ijaz Hussain, 2013. "A new approach to choose acceptance cutoff for approximate Bayesian computation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(4), pages 862-869.
    2. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    3. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
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