Importance is Important: Generalized Markov Chain Importance Sampling Methods
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Abstract (arXiv)
We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient, and rejection-free Markov chain Monte Carlo (MCMC) sampling scheme. By further leveraging the importance sampling perspective on Metropolis--Hastings algorithms, we propose an alternative MCMC sampler on discrete spaces that is also outside the Metropolis--Hastings framework, along with a general theory on its complexity. Numerical examples suggest that the proposed algorithms are consistently more efficient than the original Metropolis--Hastings versions.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 9 of its 57 references that are in the map. First posted on arXiv 13 Apr 2023.
Builds on
9 of 57 references.
References · 9
- 2021Oops I Took A Gradient: Scalable Sampling for Discrete Distributionscited by 92
- 2019The Barker proposal: combining robustness and efficiency in gradient-based MCMCcited by 20
- 2015On the Computational Complexity of High-Dimensional Bayesian Variable Selectioncited by 18
- 2015The Hamming Ball Samplercited by 16
- 2018Scalable Importance Tempering and Bayesian Variable Selectioncited by 9
- 2018Markov Chain Importance Sampling -- a highly efficient estimator for MCMCcited by 6
- 2021Dimension-free Mixing for High-dimensional Bayesian Variable Selectioncited by 6
- 2022Improving multiple-try Metropolis with local balancingcited by 5
- 2022Rapidly Mixing Multiple-try Metropolis Algorithms for Model Selection Problemscited by 4
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Citing papers per year: 2025: 1.
1 paper.