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.

Bayesian model updating of nonlinear systems using nonlinear normal modes

“…Note that computation of evidence is usually a challenging task; however, the implemented TMCMC algorithm is capable of providing model evidence as a by‐product with no additional computation cost. Recent studies have shown that the TMCMC method provides slightly biased estimates for the evidence . However, such bias does not affect the qualitative results presented in this paper because the evidence estimates for each model class are far apart, as denoted in Table .…”

Hierarchical Stochastic Model in Bayesian Inference for Engineering Applications: Theoretical Implications and Efficient Approximation

“…For each EIM basis, 2500 posterior samples of LJ and σ LJ are recorded to be used in the post-processing step of our HSM analysis. We use BASIS to draw the samples because it is highly parallel and the evidence is a by-product of the algorithm [31]. Then, we draw the posterior samples of the hyperparameters ψ with the post-processing step in our method.…”

“…The marginalized posterior of θ is estimated by substituting Equation 39 and 41 into Equation 31, which we substitute ψ by σ y :…”

Langevin Diffusion for Population Based Sampling with an Application in Bayesian Inference for Pharmacodynamics

“…In the original TMCMC the MCMC is performed for each unique sample inΘ j+1 with chain length equal to number of occurrences of the sample. In [40] it is shown that in order for the bias to be reduced all samples iñ Θ j+1 should perform an MCMC step with chain length equal to a parameter max , which is usually set to 1. The improved algorithm is called BASIS and an efficient implementation can be found in the Π4U framework [18].…”