Adaptive variant of the BUS approach to Bayesian updating

The BUS approach is a recently proposed method [1] for Bayesian updating of models with structural reliability techniques. Especially for high-dimensional problems, the combination of BUS with subset simulation [2] is shown to be efficient in drawing samples from the posterior distribution. The BUS approach can be considered an extension of rejection sampling, where a standard uniform random variable is added to the space of random variables. Each generated sample from this extended random variable space is accepted if the sample of the uniform random variable is smaller than the likelihood function scaled by a constant c. The constant c has to be selected such that it's reciprocal is not smaller than the maximum of the likelihood function. For 1/c considerably larger than the maximum of the likelihood function, the efficiency of the approach decreases. However, in many cases the maximum of the likelihood function is not known in advance. In this contribution, we propose a technique for adaptively selecting the parameter c. This causes the rejection/acceptance criterion to change throughout the simulation. The proposed approach is compared to the TMCMC method proposed by Ching and Chen in [3] by means of a numerical example. We show that the proposed approach maintains the efficiency of BUS for problems with many random variables.