Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C. Fast Langevin based algorithm for MCMC in high dimensions. (English) Zbl 1373.60053 Ann. Appl. Probab. 27, No. 4, 2195-2237 (2017). Summary: We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension \(d\). The improved complexity is \(\mathcal{O}(d^{1/5})\) compared to the complexity \(\mathcal{O}(d^{1/3})\) of the standard approach. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate (with asymptotical value 0.704), independently of the target distribution. Numerical experiments confirm our theoretical findings. Cited in 10 Documents MSC: 60F05 Central limit and other weak theorems 65C05 Monte Carlo methods Keywords:weak convergence; Markov chain Monte Carlo; diffusion limit; exponential ergodicity PDFBibTeX XMLCite \textit{A. Durmus} et al., Ann. Appl. Probab. 27, No. 4, 2195--2237 (2017; Zbl 1373.60053) Full Text: DOI arXiv Euclid