Drawing Parallels between Statistics and Nature

An Introduction to My Research

Hirofumi Shiba

D3, Institute of Statistical Mathematics

9/02/2025

Keywords in My Research

Distribution: Key of New Science

A Computational Reinterpretation

Development in Monte Carlo Methods

Markov Chain

Diffusion

Jump Process

What’s Wrong with Diffusion?

Equilibrium ≒ Reversibility

Langevin Diffusion represents a particle in a medium.

E.g. A sugar particle in a coffee

• Nature is not necessarily efficient.

  E.g. Would you wait until the sugar dissolves? To have a cup of coffee?

• It’s difficult to simulate.

What’s New in PDMP?

Irreversibility & Acceleration

• Ballistic motion, up until a turn

  E.g. Stirring coffee with a spoon

• No artificial symmetry (e.g. detailed balance)

  Fast convergence & reduced computational cost

All with a new strategy of simulation, which seems to be very efficient (ongoing research)

PDMP Package

Piecewise Deterministic Markov Process

Python

pip install pdmp-jax

Julia

] add PDMPFlux

Bringing Science Back