Parallelizing MCMC via Weierstrass Sampler
This addresses the need for efficient parallel MCMC methods in large-scale statistical analysis, though it appears incremental as it builds on existing subset-based approaches.
The paper tackles the challenge of scaling MCMC for large Bayesian problems by proposing a Weierstrass sampler that approximates full posterior samples by combining independent subset MCMC chains, achieving higher computational efficiency with competitive performance in simulations compared to methods like averaging and kernel smoothing.
With the rapidly growing scales of statistical problems, subset based communication-free parallel MCMC methods are a promising future for large scale Bayesian analysis. In this article, we propose a new Weierstrass sampler for parallel MCMC based on independent subsets. The new sampler approximates the full data posterior samples via combining the posterior draws from independent subset MCMC chains, and thus enjoys a higher computational efficiency. We show that the approximation error for the Weierstrass sampler is bounded by some tuning parameters and provide suggestions for choice of the values. Simulation study shows the Weierstrass sampler is very competitive compared to other methods for combining MCMC chains generated for subsets, including averaging and kernel smoothing.