The Acceptance Probability of the Hybrid Monte Carlo Method in High-Dimensional Problems

A. Beskos, N. S. Pillai, G. O. Roberts, J. M. Sanz-Serna, A. M. Stuart, Theodore E. Simos, George Psihoyios, Ch. Tsitouras
We investigate the properties of the Hybrid Monte-Carlo algorithm in high dimensions. In the simplified scenario of independent, identically distributed components, we prove that, to obtain an O(1) acceptance probability as the dimension d of the state space tends to ∞, the Verlet/leap-frog step-size h should be scaled as h = × d −1/4 . We also identify analytically the asymptotically optimal acceptance probability, which turns out to be 0.651 (with three decimal places); this is the choice
more » ... s is the choice that optimally balances the cost of generating a proposal, which decreases as increases, against the cost related to the average number of proposals required to obtain acceptance, which increases as increases.
doi:10.1063/1.3498436 fatcat:j7woefrafvafvkl4vj63wue2c4