Erratum to “A comparison of generalized hybrid Monte Carlo methods with and without momentum flip” [J. Comput. Phys. 228 (2009) 2256–2265]

✍ Scribed by Elena Akhmatskaya; Nawaf Bou-Rabee; Sebastian Reich

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 380 KB
• Volume: 228
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2009.06.039

✦ Synopsis

This note is to point out an error in the theory part of the publication [1]. We will follow the notations and definitions of [1] unless stated otherwise.

Contrary to what is claimed in Section 2.2 of [1], the modified Metropolis-Hastings acceptance criterion (Eq. ( 6) in [1].)

does not satisfy a modified detailed balance condition for the choice of a linear involution F and for the choice of dðC 0 ; CÞ suggested in the paper. We will produce the mathematical reasons below, which were kindly pointed out to us by Tony Lelievre and Gabriel Stoltz. We will also produce numerical evidence that despite not being able to preserve a (modified) detailed balance condition, the proposed GHMC method without momentum flip produces better results in terms of sampling accuracy than corresponding results from a method without any Metropolis-Hasting correction step, i.e., a standard discretization of the underlying second-order Langevin dynamics. We also find a good agreement between GHMC with momentum flip (rigorous sampling from canonical distribution) and without momentum flip in terms of sampling accuracy for acceptance rates above 75-80%.