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The Barker proposal: Combining robustness and efficiency in gradient-based MCMC.

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Summary
This summary is machine-generated.

We introduce a novel gradient-based Markov chain Monte Carlo (MCMC) algorithm that enhances robustness to tuning parameters. This new MCMC method balances the efficiency of gradient-based approaches with the reliability of simpler algorithms.

Keywords:
Bayesian computationMCMCMetropolis–Hastingsadaptive tuningspectral gap

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Area of Science:

  • Computational Statistics
  • Markov Chain Monte Carlo (MCMC) Methods
  • Bayesian Inference

Background:

  • Designing Markov chain Monte Carlo (MCMC) algorithms involves a trade-off between robustness and computational efficiency.
  • Sophisticated MCMC algorithms often exhibit increased sensitivity to tuning parameters like step-size and reduced robustness to distributional heterogeneity.
  • Spectral gap analysis reveals how algorithm performance degrades with suboptimal step-size choices.

Purpose of the Study:

  • To develop a novel MCMC algorithm with improved robustness to tuning parameters.
  • To address the tension between robustness and efficiency in MCMC sampling.
  • To enhance the performance of adaptive MCMC methods.

Main Methods:

  • Proposed a novel gradient-based MCMC algorithm inspired by the Barker accept-reject rule.
  • Analyzed spectral gap behavior to characterize robustness to step-size parameters.
  • Conducted theoretical analysis on tuning robustness, geometric ergodicity, and dimensional scaling.
  • Performed numerical simulations, including comparisons with state-of-the-art adaptive MCMC methods.

Main Results:

  • The proposed MCMC algorithm demonstrates enhanced robustness to tuning parameters compared to existing sophisticated methods.
  • Theoretical results indicate a favorable combination of robustness and efficiency, akin to simple yet efficient gradient-based schemes.
  • Numerical experiments confirm the algorithm's superior performance, particularly within adaptive MCMC frameworks.

Conclusions:

  • The novel gradient-based MCMC algorithm successfully integrates the robustness of simpler methods with the efficiency of gradient-based techniques.
  • This approach offers significant advantages in scenarios demanding high robustness, especially in adaptive MCMC applications.
  • The findings suggest a promising direction for developing more reliable and efficient MCMC samplers.