A Provable Comparison Scheme via Scaling Limits for Emerging Monte Carlo Samplers

概要

A class of Monte Carlo methods with a qualitatively different dynamical nature from traditional MCMC methods is emerging within the framework of piecewise deterministic Markov processes (PDMPs). Its design space is begin actively explored, and our work aims to provide theoretical grounding for comparing their performance. We propose to measure their performance by examing their log-likelihood processes, and prove a theoretically rigorous ordering of asymptotic efficiency between algorithms, through scaling analysis and weak convergence results. Specifically, within this framework, Forward Event-Chain Monte Carlo (FECMC) is asymptotically more efficient than Bouncy Particle Sampler (BPS), regardless of the choice of hyperparameters. Moreover, we show that FECMC attains its best efficiency when this hyperparameter is set to zero, showing its design choices successfully lead to a robust exploration of the target distribution.

ISBA World Meeting 2026

Date	Location
Jun. 28-Jul. 2, 2026	WINC AICHI (Aichi Industry & Labor Center)

Citation

BibTeX citation:

@online{shiba2026,
  author = {Shiba, Hirofumi},
  title = {A {Provable} {Comparison} {Scheme} via {Scaling} {Limits} for
    {Emerging} {Monte} {Carlo} {Samplers}},
  date = {2026-06-28},
  url = {https://162348.github.io/posts/2025/Posters/ISBA.html},
  langid = {en},
  abstract = {A class of Monte Carlo methods with a qualitatively
    different dynamical nature from traditional MCMC methods is emerging
    within the framework of piecewise deterministic Markov processes
    (PDMPs). Its design space is begin actively explored, and our work
    aims to provide theoretical grounding for comparing their
    performance. We propose to measure their performance by examing
    their log-likelihood processes, and prove a theoretically rigorous
    ordering of asymptotic efficiency between algorithms, through
    scaling analysis and weak convergence results. Specifically, within
    this framework, Forward Event-Chain Monte Carlo (FECMC) is
    asymptotically more efficient than Bouncy Particle Sampler (BPS),
    regardless of the choice of hyperparameters. Moreover, we show that
    FECMC attains its best efficiency when this hyperparameter is set to
    zero, showing its design choices successfully lead to a robust
    exploration of the target distribution.}
}

For attribution, please cite this work as:

Shiba, H. (2026, June 28). A Provable Comparison Scheme via Scaling Limits for Emerging Monte Carlo Samplers.