2016/10/03 by Richard A. Norton, Norton, Richard A., Colin Fox +1
Mathematics · Physics and Astronomy · #62M05 #65C40 #65Y20 #68Q87 #68W20 #Applied mathematics #Autoregressive model #Bayesian probability #Computation (stat.CO) #Computer science #Econometrics #FOS: Computer and information sciences #FOS: Mathematics #Hamiltonian (control theory) #Langevin dynamics #Langevin equation #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Mathematical optimization #Mathematics #Physics #Probability (math.PR) #Statistical physics #Statistics #Theoretical and Computational Physics #math.PR #msc:60J05 #msc:60J22 #msc:62M05 #msc:65C40 #msc:65Y20 #msc:68Q87 #msc:68W20 #primary 60J22 #secondary 60J05 #stat.CO
paper · pdf · doi:10.48550/arxiv.1610.00781
published in arXiv (Cornell University) (Cornell University) · 44 pages, 1 figure. arXiv admin note: text overlap with arXiv:1605.05441
arxiv created 2016/10/03 · openalex publication_date 2016/10/03 · arxiv updated 2016/10/05 · openalex created_date 2016/10/14 · openalex updated_date 2026/07/28
Proposals for Metropolis-Hastings MCMC derived by discretizing Langevin diffusion or Hamiltonian dynamics are examples of stochastic autoregressive proposals that form a natural wider class of proposals with equivalent computability. We analyze Metropolis-Hastings MCMC with stochastic autoregressive proposals applied to target distributions that are absolutely continuous with respect to some Gaussian distribution to derive expressions for expected acceptance probability and expected jump size, as well as measures of computational cost, in the limit of high dimension. Thus, we are able to unify existing analyzes for these classes of proposals, and to extend the theoretical results that provide useful guidelines for tuning the proposals for optimal computational efficiency. For the simplified Langevin algorithm we find that it is optimal to take at least three steps of the proposal before the Metropolis-Hastings accept-reject step, and for Hamiltonian/hybrid Monte Carlo we provide new guidelines for the optimal number of integration steps and criteria for choosing the optimal mass matrix.