The penalty method for random walks with uncertain energies

D. M. Ceperley, M. Dewing

Research output: Contribution to journalArticlepeer-review


We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed quantum-classical simulations. If the noise is normally distributed, we are able to modify the acceptance probability by applying a penalty to the energy difference and thereby achieve exact sampling even with very strong noise. When one has to estimate the variance we have an approximate formula, good in the limit of a large number of independent estimates. We argue that the penalty method is nearly optimal. We also adapt an existing method by Kennedy and Kuti and compare to the penalty method on a one-dimensional double well.

Original languageEnglish (US)
Pages (from-to)9812-9820
Number of pages9
JournalJournal of Chemical Physics
Issue number20
StatePublished - May 22 1999

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry


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