126 citations · 826 across the 40 of their papers we have counts for
23 papers · 1 filter
Provable Non-Acceleration of Standard Strang Splittings of Kinetic Langevin Dynamics
Nawaf Bou-Rabee
The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Carlo algorithms. Under a suitabl…
On couplings for kinetic Langevin diffusions
Nawaf Bou-Rabee, Sonja Cox, Roy Schieven
For the kinetic Langevin diffusion and its splitting discretizations, the hypoelliptic noise structure makes the relationship between couplings and total variation (TV) bounds more…
From Continuous to Discrete: a No-U-Turn Sampler for Permutations
Nawaf Bou-Rabee, Zichu Wang
We introduce a discrete-space analogue of the No-U-Turn sampler on the symmetric group , yielding a locally adaptive and reversible Markov chain Monte Carlo method for $\mathr…
Decoupling for Markov Chains
Nawaf Bou-Rabee, Victor H. de la Peña
Consider a Markov chain with invariant measure that admits the representation , where are i.i.d. random variables and is…
Ballistic Convergence in Hit-and-Run Monte Carlo and a Coordinate-free Randomized Kaczmarz Algorithm
Nawaf Bou-Rabee, Andreas Eberle, Stefan Oberdörster
Hit-and-Run is a coordinate-free Gibbs sampler, yet the quantitative advantages of its coordinate-free property remain largely unexplored beyond empirical studies. In this paper, w…
Mixing of the No-U-Turn Sampler and the Geometry of Gaussian Concentration
Nawaf Bou-Rabee, Stefan Oberdörster
We prove that the mixing time of the No-U-Turn Sampler (NUTS), when initialized in the concentration region of the canonical Gaussian measure, scales as , up to logarithmi…
Nonlinear Hamiltonian Monte Carlo & its Particle Approximation
Nawaf Bou-Rabee, Katharina Schuh
We present a nonlinear (in the sense of McKean) generalization of Hamiltonian Monte Carlo (HMC) termed nonlinear HMC (nHMC) capable of sampling from nonlinear probability measures…
Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime
Nawaf Bou-Rabee, Stefan Oberdörster
We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The ap…
Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integration
Nawaf Bou-Rabee, Milo Marsden
A randomized time integrator is suggested for unadjusted Hamiltonian Monte Carlo (uHMC) which involves a very minor modification to the usual Verlet time integrator, and hence, is…
Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlo
Nawaf Bou-Rabee, Andreas Eberle
We provide quantitative upper bounds on the total variation mixing time of the Markov chain corresponding to the unadjusted Hamiltonian Monte Carlo (uHMC) algorithm. For two genera…
Couplings for Andersen Dynamics
Nawaf Bou-Rabee, Andreas Eberle
Andersen dynamics is a standard method for molecular simulations, and a precursor of the Hamiltonian Monte Carlo algorithm used in MCMC inference. The stochastic process correspond…
Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models
Nawaf Bou-Rabee, Katharina Schuh
We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of…
Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions
Nawaf Bou-Rabee, Andreas Eberle
We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequenc…
Coupling and Convergence for Hamiltonian Monte Carlo
Nawaf Bou-Rabee, Andreas Eberle, Raphael Zimmer
Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein)…
Geometric integrators and the Hamiltonian Monte Carlo method
Nawaf Bou-Rabee, Jesús María Sanz-Serna
This paper surveys in detail the relations between numerical integration and the Hamiltonian (or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies i…
Cayley Splitting for Second-Order Langevin Stochastic Partial Differential Equations
Nawaf Bou-Rabee
We give accurate and ergodic numerical methods for semilinear, second-order Langevin stochastic partial differential equations (SPDE). As a byproduct, we also give good geometric n…
SPECTRWM: Spectral Random Walk Method for the Numerical Solution of Stochastic Partial Differential Equations
Nawaf Bou-Rabee
The numerical solution of stochastic partial differential equations (SPDE) presents challenges not encountered in the simulation of PDEs or SDEs. Indeed, the roughness of the noise…
Randomized Hamiltonian Monte Carlo
Nawaf Bou-Rabee, Jesus Maria Sanz-Serna
Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality,…
Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations
Nawaf Bou-Rabee, Eric Vanden-Eijnden
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics…
Non-asymptotic mixing of the MALA algorithm
Nawaf Bou-Rabee, Martin Hairer, Eric Vanden-Eijnden
The Metropolis-Adjusted Langevin Algorithm (MALA), originally introduced to sample exactly the invariant measure of certain stochastic differential equations (SDE) on infinitely lo…
Ballistic Transport at Uniform Temperature
Nawaf Bou-Rabee, Houman Owhadi
A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations…
Ergodicity of Langevin Processes with Degenerate Diffusion in Momentums
Nawaf Bou-Rabee, Houman Owhadi
This paper introduces a geometric method for proving ergodicity of degenerate noise driven stochastic processes. The driving noise is assumed to be an arbitrary Levy process with n…
Stochastic Variational Integrators
Nawaf Bou-Rabee, Houman Owhadi
This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds. The main result is to derive stochastic governing equations for suc…