TY - JOUR

T1 - Optimal scaling of discrete approximations to Langevin diffusions.

AU - Roberts, G. O.

AU - Rosenthal, J. S.

PY - 1998

Y1 - 1998

N2 - We consider the optimal scaling problem for proposal distributions in Hastings–Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that, as a function of dimension n, the complexity of the algorithm is O(n1/3), which compares favourably with the O(n) complexity of random walk Metropolis algorithms. We illustrate this comparison with some example simulations.

AB - We consider the optimal scaling problem for proposal distributions in Hastings–Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that, as a function of dimension n, the complexity of the algorithm is O(n1/3), which compares favourably with the O(n) complexity of random walk Metropolis algorithms. We illustrate this comparison with some example simulations.

KW - Hastings–Metropolis algorithm • Langevin algorithm • Markov chain Monte Carlo method • Weak convergence

U2 - 10.1111/1467-9868.00123

DO - 10.1111/1467-9868.00123

M3 - Journal article

VL - 60

SP - 255

EP - 268

JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

SN - 1369-7412

IS - 1

ER -