Research
Interests
My current research interests are situated in the overlap between probability and applied mathematics. In addition to the papers linked below, these interests are reflected on mathoverflow. As of late, I have been working on Markov chain mixing time, stochastic differential equations, piecewise deterministic Markov processes, and couplings, among other topics. The stochastic models considered in my research works often display high-dimensionality, multi-modality, multi-scale behavior, and/or other characteristics that frequently present themselves in applications.
Selected Papers
- GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlo, N. Bou-Rabee, B. Carpenter & M. Marsden, 2024.
- Randomized Runge-Kutta Nyström, N. Bou-Rabee & T. S. Kleppe, Submitted, 2023.
- Nonlinear Hamiltonian Monte Carlo and its Particle Approximation, N. Bou-Rabee & K. Schuh, Submitted, 2023.
- Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime, N. Bou-Rabee & S. Oberdörster, Submitted, 2023.
- Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integration, N. Bou-Rabee & M. Marsden, Submitted, 2023.
- Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlo, N. Bou-Rabee & A. Eberle, Bernoulli, Vol. 29, pp. 75-104, 2023.
- Convergence of Unadjusted Hamiltonian Monte Carlo for mean-field models, N. Bou-Rabee & K. Schuh, Electronic Journal of Probability, Vol. 28, paper no. 91, pp. 1-40, 2023.
- Couplings for Andersen Dynamics, N. Bou-Rabee & A. Eberle, Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques, Vol. 58, No. 2, pp. 916-944, 2022.
- Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions, N. Bou-Rabee & A. Eberle, Stoch PDE: Anal Comp, Vol. 9, pp. 207-242, 2021.
- Coupling and Convergence for Hamiltonian Monte Carlo, N. Bou-Rabee, A. Eberle, and R. Zimmer, Annals of Applied Probability, Vol. 30, No. 3, pp. 1209-1250, 2020.
- Sticky Brownian Motion and its Numerical Solution, N. Bou-Rabee and M. Holmes-Cerfon, SIAM Review, Vol. 62, No. 1, pp. 164-195, 2020.
- Geometric Integrators and the Hamiltonian Monte Carlo Method, N. Bou-Rabee, J. M. Sanz-Serna, Acta Numerica, , Vol. 27, pp. 113-206, 2018.
- Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations N. Bou-Rabee & E. Vanden-Eijnden, Memoirs of the American Mathematical Society, Vol. 256, 2018.
- Randomized Hamiltonian Monte Carlo, N. Bou-Rabee, J. M. Sanz-Serna, Annals of Applied Probability, Vol. 27, No. 4, pp. 2159-2194, 2017.