Computational Complexity Comparison via Scaling Limits for Emerging MCMC Samplers

Hirofumi Shiba

ISM (3rd year PhD Student)

2/10/2026

1 What is a PDMP?

An illustration of a Piecewise Deterministic Markov Process.
Output from the PDMPFlux.jl package.

A Blog Entry on Bayesian Computation by an Applied Mathematician

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1.1 Evolution of Monte Carlo

Markov Chain
(1953–)

Diffusion
(1978–)

PDMP
(2008–)

1.2 Piecewise Deterministic Markov Process

Takeaway: PDMP ≒ ODE + Jump

Langevin Diffusion

Randomized Hamiltonian Monte Carlo

1.3 Which One is Faster ?

Zig-Zag Sampler
(Bierkens et al., 2019)

Bouncy Particle Sampler
(Bouchard-Côté et al., 2018)

Forward Event-Chain Monte Carlo
(Michel et al., 2020)

1.4 ESS Comparison

1.5 ESS: Theory vs. Numerical Results

1.6 New Asymptotic Variance Estimator