Bayes Reading Group: Nawaf Bou-Rabee (Rutgers, Flatiron, & Wharton)

Friday Dec 5, 2025, 11:00 AM → 12:00 PM America/New_York

3rd Floor Conference Room (162 Fifth Avenue)

Discussion lead: Nawaf Bou-Rabee (Rutgers, Flatiron, & Wharton)

Title: When the Kinetic Energy Doesn’t Budge: Isokinetic Monte Carlo in Theory and Practice

Abstract: Iso-kinetic HMC is an elegant and somewhat overlooked variant of Hamiltonian Monte Carlo dating back to the foundational work of Martyna, Minary and Tuckerman in the early 2000s. Unlike classical HMC, iso-kinetic HMC evolves under a non-holonomic constraint that locks the kinetic energy to a fixed value. In other words, instead of letting the instantaneous temperature fluctuate as in standard HMC, the sampler “rides a geodesic” on a constant-kinetic-energy manifold. This constraint fundamentally alters the geometry of the dynamics, and as a result leads to markedly different statistical and numerical behavior.

The method resurfaced a decade later in the influential work of Fang, Sanz-Serna, and Skeel, who placed iso-kinetic dynamics within the broader framework of compressible generalized HMC. And in the last year, it has re-entered the spotlight in Bayesian computation, in recent work by Robnik, Cohn-Gordon, and Seljak exploring its surprising empirical performance in high-dimensional inference problems.

This journal club talk will revisit iso-kinetic HMC from first principles, examining why the method is reversible, how the non-holonomic constraint interacts with ergodicity and volume preservation, and whether the fixed-kinetic-energy geometry provides a form of implicit preconditioning. We will also discuss what is known (and what remains mysterious) about its scaling in high dimension, and how its tuning behavior compares with standard HMC and NUTS.

Selected References:

• Martyna, Minary & Tuckerman (2003a). Algorithms and novel applications based on the isokinetic ensemble. I. Biophysical and path integral molecular dynamics. J. Chem. Phys.

• Minary, Martyna & Tuckerman (2003b). Algorithms and novel applications based on the isokinetic ensemble. II. Ab initio molecular dynamics. J. Chem. Phys.

• Tuckerman (2010). Statistical Mechanics: Theory and Molecular Simulation, Chapter 4 

• Fang, Sanz-Serna & Skeel (2014). Compressible generalized hybrid Monte Carlo. J. Chem. Phys. 

Robnik, Cohn-Gordon & Seljak (2025). Metropolis-adjusted Microcanonical Hamiltonian Monte Carlo. arXiv:2503.01707.