# Parallelizing MCMC via Weierstrass Sampler

arXiv: https://arxiv.org/abs/1312.4605 · HTML: https://mlsanity.com/paper/1312.4605/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2013.

## Built on by (most cited first, 11 of 11)

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- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [On Convergence of Federated Averaging Langevin Dynamics](https://mlsanity.com/paper/2112.05120/) (2021)
- [DG-LMC: A Turn-key and Scalable Synchronous Distributed MCMC Algorithm via Langevin Monte Carlo within Gibbs](https://mlsanity.com/paper/2106.06300/) (2021)
- [Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling](https://mlsanity.com/paper/2111.14008/) (2021)
- [Sharded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2306.00361/) (2023)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Federated Averaging Langevin Dynamics: Toward a unified theory and new algorithms](https://mlsanity.com/paper/2211.00100/) (2022)
- [Vertical Consensus Inference for High-Dimensional Random Partition](https://mlsanity.com/paper/2603.27864/) (2026)
- [Measuring the right thing: justifying metrics in AI impact assessments](https://mlsanity.com/paper/2504.05007/) (2025)
- [Neural composite likelihood estimation: simulation based inference for time series](https://mlsanity.com/paper/2609.21762/) (2026)

## Abstract (arXiv)

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.