Langevin-based Markov chain Monte Carlo (MCMC) algorithms use gradient information to improve sampling, particularly in high dimensions. Classical optimal scaling theory for these algorithms has largely focused on the Metropolis-Hastings (MH) acceptance rule. However, there has been a recent surge in acceptance rules beyond MH for applications spanning differential privacy, stochastic MCMC, diffusion models, and molecular dynamics. We develop optimal scaling results for Langevin proposals employed with generalized acceptance rules belonging to a suitable class. For high-dimensional targets, we recover the usual $O(d^{-1/3})$ scaling, while different acceptance rules lead to different optimal acceptance probabilities.
Exact reversible locally adaptive step sizes are introduced by Bou-Rabee et al. (2026) in the context of the No-U-Turn Hamiltonian Monte Carlo (HMC) sampler for the purpose of high performance HMC sampling in challenging target distributions. This paper carefully explains and illustrates the locally adaptive step size...
Jimmy Huy Tran, Tore Selland Kleppe, Nawaf Bou-Rabee· 0 citations
Reversible Jump Markov Chain Monte Carlo (RJMCMC) is a principled framework for Bayesian model comparison, but its practical use is often limited due to the difficulty of designing between-model proposals that reach regions of high posterior probability. In addition, its inherently sequential nature limits efficient us...
Experiments on logistic regression, probabilistic matrix factorization, and Bayesian neural networks show that HyperMC improves posterior approximation or predictive calibration relative to MAMBA, grid search, and heuristic baselines, while Robust HyperMC yields more stable and reproducible tuning results.
Event-chain Monte Carlo (ECMC) has revolutionised computational sampling over recent years, providing a powerful alternative to the molecular-dynamics (MD) and Hamiltonian Monte Carlo (HMC) algorithms. Each method outperforms the ubiquitous random-walk Metropolis algorithm by advancing particles along deterministic tra...
James Gulliford, Gareth O. Roberts, Michael F. Faulkner· 0 citations
We characterize the high-dimensional convergence of the arithmetic mean from the independence Metropolis-Hastings algorithm initialized at its proposal. Convergence is measured in the worst-case expected absolute error over bounded functions. We prove necessary and sufficient conditions for the mean to converge in rela...
Nii-MALA is introduced, a high-performance C implementation of the Metropolis-Adjusted Langevin Algorithm, which leverages Message Passing Interface for parallelization and incorporates automatic differentiation backends for gradient evaluation and benchmark it against several other codes using radial velocity data fro...
Jia-Men Jiao, Sheng Jin, Wen-Xin Jiang et al.· Publications of the Astronom...· 0 citations
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