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Preprint
Unbiased estimation of equilibrium, rates, and committors from Markov state model analysis
27 May 2021
Abstract
Markov state models (MSMs) have been broadly adopted for analyzing molecular
dynamics trajectories, but the approximate nature of the models that results
from coarse-graining into discrete states is a long-known limitation. We show
theoretically that, despite the coarse graining, in principle MSM-like analysis
can yield unbiased estimation of key observables. We describe unbiased
estimators for equilibrium state populations, for the mean first-passage time
(MFPT) of an arbitrary process, and for state committors - i.e., splitting
probabilities. Generically, the estimators are only asymptotically unbiased but
we describe how extension of a recently proposed reweighting scheme can
accelerate relaxation to unbiased values. Exactly accounting for 'sliding
window' averaging over finite-length trajectories is a key, novel element of
our analysis. In general, our analysis indicates that coarse-grained MSMs are
asymptotically unbiased for steady-state properties only when appropriate
boundary conditions (e.g., source-sink for MFPT estimation) are applied
directly to trajectories, prior to calculation of the appropriate transition
matrix.
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Details
- Title
- Unbiased estimation of equilibrium, rates, and committors from Markov state model analysis
- Creators
- John D RussoJeremy CoppermanDavid AristoffGideon SimpsonDaniel M Zuckerman
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991019296797204721