Bayesian Annealed Sequential Importance Sampling: An Unbiased Version of Transitional Markov Chain Monte Carlo

Abstract

The transitional Markov chain Monte Carlo (TMCMC) is one of the efficient algorithms for performing Markov chain Monte Carlo (MCMC) in the context of Bayesian uncertainty quantification in parallel computing architectures. However, the features that are associated with its efficient sampling are also responsible for its introducing of bias in the sampling. We demonstrate that the Markov chains of each subsample in TMCMC may result in uneven chain lengths that distort the intermediate target distributions and introduce bias accumulation in each stage of the TMCMC algorithm. We remedy this drawback of TMCMC by proposing uniform chain lengths, with or without burn-in, so that the algorithm emphasizes sequential importance sampling (SIS) over MCMC. The proposed Bayesian annealed sequential importance sampling (BASIS) removes the bias of the original TMCMC and at the same time increases its parallel efficiency. We demonstrate the advantages and drawbacks of BASIS in modeling of bridge dynamics using finite elements and a disk-wall collision using discrete element methods.