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Comparing Markov Chain Samplers for Molecular Simulation

Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA
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Author to whom correspondence should be addressed.
Current address: School of Mathematical and Statistical Sciences, Arizona State University, Phoenix, Tempe, AZ 85287, USA.
Entropy 2017, 19(10), 561; https://doi.org/10.3390/e19100561
Received: 6 September 2017 / Revised: 17 October 2017 / Accepted: 19 October 2017 / Published: 21 October 2017
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
Markov chain Monte Carlo sampling propagators, including numerical integrators for stochastic dynamics, are central to the calculation of thermodynamic quantities and determination of structure for molecular systems. Efficiency is paramount, and to a great extent, this is determined by the integrated autocorrelation time (IAcT). This quantity varies depending on the observable that is being estimated. It is suggested that it is the maximum of the IAcT over all observables that is the relevant metric. Reviewed here is a method for estimating this quantity. For reversible propagators (which are those that satisfy detailed balance), the maximum IAcT is determined by the spectral gap in the forward transfer operator, but for irreversible propagators, the maximum IAcT can be far less than or greater than what might be inferred from the spectral gap. This is consistent with recent theoretical results (not to mention past practical experience) suggesting that irreversible propagators generally perform better if not much better than reversible ones. Typical irreversible propagators have a parameter controlling the mix of ballistic and diffusive movement. To gain insight into the effect of the damping parameter for Langevin dynamics, its optimal value is obtained here for a multidimensional quadratic potential energy function. View Full-Text
Keywords: Markov chain Monte Carlo; stochastic dynamics integrators; decorrelation time; integrated autocorrelation time Markov chain Monte Carlo; stochastic dynamics integrators; decorrelation time; integrated autocorrelation time
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Skeel, R.D.; Fang, Y. Comparing Markov Chain Samplers for Molecular Simulation. Entropy 2017, 19, 561.

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