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 rareevent simulation, first developed in S. K. Au and J. L. Beck [Probabilistic Engrg. Mech., 16 (2001), pp. 263277]. It has been named ABCSubSim. 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 realworld 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 ABCSubSim readily provides an estimate of the evidence (marginal likelihood) for posterior model class assessment, as a byproduct.
Original language  English 

Pages (fromto)  1339–1358 
Number of pages  20 
Journal  SIAM Journal on Scientific Computing 
Volume  36 
Issue number  3 
DOIs  
Publication status  Published  26 Jun 2014 
Keywords
 approximate Bayesian computation
 subset simulation
 Bayesian inverse problem
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Extraordinary PhD Award
ChiachioRuano, Juan (Recipient), Nov 2018
Prize: Prize (including medals and awards)