Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces
By R. Assaraf, Michel Caffarel. 2003
129 citations recorded by the source corpus.
A simple and stable method for computing accurate expectation values of observables with variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual “bare” estimator associated with the observable by an improved or “renormalized” estimator. Using this estimator more accurate averages are obtained: Not only the statistical fluctuations are reduced but also the systematic error (bias) associated with the approximate VMC or (fixed-node) DMC probability densities. It is shown that improved estimators obey a zero-variance zero-bias property similar to the usual zero-variance zero-bias property of the energy with the local energy as improved estimator. Using this property improved estimators can be optimized and the resulting accuracy on expectation values may reach the remarkable accuracy obtained for total energies. As an important example, we present the application of our formalism to the computation of forces in molecular systems. Cal...
Subfields: Atomic and Molecular Physics, and Optics, Biomedical Engineering, Statistical and Nonlinear Physics
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- Chris J. Oates
- Antonietta Mira
- Nicolas Chopin
- Reza Solgi
- D. Imparato
- Mark A. Girolami
- Ying Nian Wu
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Citations in the corpus
- Control functionals for Monte Carlo integration (2014, methodology): “These control variates were explored in the case where φ is a (gradient of a low degree) polynomial by Assaraf and Caffarel (1999, 2003) and Mira et al., (2013).”
- Zero variance Markov chain Monte Carlo for Bayesian estimators (2010, methodology): “In [4,5] unbiasedness and existence of a central limit theorem (CLT) for the ZV estimator are not discussed, neither in [28], where this estimator is applied to a toy example.”