An efficient and robust sampler for Bayesian inference: Transitional Ensemble Markov Chain Monte Carlo

Abstract

Bayesian inference is a popular approach towards parameter identification in engineering problems. Such technique would involve iterative sampling methods which are often robust. However, these sampling methods often require significant computational resources and also the tuning of a large number of parameters. This motivates the development of a sampler called the Transitional Ensemble Markov Chain Monte Carlo.The proposed approach implements the Affine-invariant Ensemble sampler in place of the classical Metropolis–Hastings sampler as the Markov chain Monte Carlo move kernel. In doing so, it allows for the sampling of badly-scaled and highly-anisotropic distributions without requiring extra computational costs. This makes the proposed sampler computationally efficient as a result of having less auxiliary parameters to compute per iteration compared to the standard single particle Transitional Markov Chain Monte Carlo. In addition to such change, an adaptive tuning algorithm is also proposed within the new sampler. This algorithm allows for automatic tuning of the step-size of the Affine-invariant Ensemble sampler. Hence, such proposals not only ensure that the new sampler is “tune-free” for the users, but also improves its robustness by ensuring that the acceptance rate of samples is well-controlled within acceptable bounds. As a result, this approach could be significantly faster compared to standard Transitional Markov Chain Monte Carlo methods on badly scaled and highly skewed distributions, which can be encountered when dealing with complex engineering problems.The proposed sampler will be implemented on 2 benchmark numerical examples of varying complexities to demonstrate its strengths and advantages. In addition, the sampler is validated by investigating its parameter identification capability on an Aluminium Frame using experimental data.