Approximate Bayesian computation by subset simulation. 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, “Estimation of small failure probabilities in high dimensions by subset simulation”, Probabilistic Engrg. Mech., 16, 263–277 (2001)]. 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.

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  1. An, Ziwen; Nott, David J.; Drovandi, Christopher: Robust Bayesian synthetic likelihood via a semi-parametric approach (2020)
  2. Chu, Liu; Shi, Jiajia; Souza de Cursi, Eduardo; Ben, Shujun: Efficiency improvement of Kriging surrogate model by subset simulation in implicit expression problems (2020)
  3. Arampatzis, Georgios; Wälchli, Daniel; Angelikopoulos, Panagiotis; Wu, Stephen; Hadjidoukas, Panagiotis; Koumoutsakos, Petros: Langevin diffusion for population based sampling with an application in Bayesian inference for pharmacodynamics (2018)
  4. Betz, Wolfgang; Papaioannou, Iason; Beck, James L.; Straub, Daniel: Bayesian inference with subset simulation: strategies and improvements (2018)
  5. Karabatsos, George; Leisen, Fabrizio: An approximate likelihood perspective on ABC methods (2018)
  6. Prangle, Dennis; Everitt, Richard G.; Kypraios, Theodore: A rare event approach to high-dimensional approximate Bayesian computation (2018)
  7. Vakilzadeh, Majid K.; Beck, James L.; Abrahamsson, Thomas: Using approximate Bayesian computation by subset simulation for efficient posterior assessment of dynamic state-space model classes (2018)
  8. DiazDelaO, F. A.; Garbuno-Inigo, A.; Au, S. K.; Yoshida, I.: Bayesian updating and model class selection with subset simulation (2017)
  9. Huang, Yong; Beck, James L.; Li, Hui: Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment (2017)
  10. Straub, Daniel; Papaioannou, Iason; Betz, Wolfgang: Bayesian analysis of rare events (2016)
  11. Hadjidoukas, P. E.; Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P.: (\Pi)4U: a high performance computing framework for Bayesian uncertainty quantification of complex models (2015)
  12. Chiachio, Manuel; Beck, James L.; Chiachio, Juan; Rus, Guillermo: Approximate Bayesian computation by subset simulation (2014)