Approximate Bayesian computation by subset simulation

Manuel Chiachio, James L. Beck, Juan Chiachio, Guillermo Rus

Research output: Contribution to journalArticle

37 Citations (Scopus)
14 Downloads (Pure)

Abstract

A new approximate Bayesian computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of subset simulation for efficient rare-event simulation, first developed in S. K. Au and J. L. Beck [Probabilistic Engrg. Mech., 16 (2001), pp. 263--277]. It has been named ABC-SubSim. The idea is to choose the nested decreasing sequence of regions in subset simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space. The efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real-world applications of ABC. We show that the proposed algorithm outperforms other recent sequential ABC algorithms in terms of computational efficiency while achieving the same, or better, measure of accuracy in the posterior distribution. We also show that ABC-SubSim readily provides an estimate of the evidence (marginal likelihood) for posterior model class assessment, as a by-product.
Original languageEnglish
Pages (from-to)1339–1358
Number of pages20
JournalSIAM Journal on Scientific Computing
Volume36
Issue number3
DOIs
Publication statusPublished - 26 Jun 2014

    Fingerprint

Keywords

  • approximate Bayesian computation
  • subset simulation
  • Bayesian inverse problem

Cite this

Chiachio, M., Beck, J. L., Chiachio, J., & Rus, G. (2014). Approximate Bayesian computation by subset simulation. SIAM Journal on Scientific Computing, 36(3), 1339–1358. https://doi.org/10.1137/130932831