Investigation of statistical error and bias in pure quantum Monte Carlo simulations of Be (bibtex)

by Allan Olley

Abstract:

The purpose of this thesis is to investigate uncontrolled statistical error and bias resulting from the tendency of a few walkers to dominate pure diffusion pure diffusion quantum Monte Carlo simulations as reported by Assaraf et al. For the system of atomic Be we employ East et al.'s and Langfelder et al.'s algorithm which shares the essential features of pure diffusion Monte Carlo but has other features designed to deal with the variance of the weights and potential bias. In order to gauge the extent to which a few walkers were dominating, the effective ensemble size ($N_{eff}$) of the simulation was monitored and the simulation reset if certain criterion depending on $N_{eff}$ were met; several reset criterion were employed in order to determine if there was any dependence of the properties estimates on the effective ensemble size, reflecting a bias. No evidence of a systematic dependence of the simulated physical properties on the effective ensemble size was found. Therefore we conclude that there is no evidence that the algorithm of East \em et al. and Langfelder \em et al. suffers from the bias problem exhibited in similar pure-diffusion quantum Monte Carlo simulations. The results of the simulation (all in atomic units) are as follows: $E_L=-14.6676(7)$, $r=5.96(2)$, $r_2=16.1(1)$, $1/r=8.35(1)$, $1/r^2=53.1(2)$, and $\alpha=38.2(9)$. These are compared to other determinants in the literature.

Reference:

Allan Olley, "Investigation of statistical error and bias in pure quantum Monte Carlo simulations of Be", 2002.

Bibtex Entry:

@bachelorsthesis{2002AO, title={Investigation of statistical error and bias in pure quantum Monte Carlo simulations of Be}, author={Allan Olley}, month={April}, year={2002}, abstract={The purpose of this thesis is to investigate uncontrolled statistical error and bias resulting from the tendency of a few walkers to dominate pure diffusion pure diffusion quantum Monte Carlo simulations as reported by Assaraf et al. For the system of atomic Be we employ East et al.'s and Langfelder et al.'s algorithm which shares the essential features of pure diffusion Monte Carlo but has other features designed to deal with the variance of the weights and potential bias. In order to gauge the extent to which a few walkers were dominating, the effective ensemble size ($N_{eff}$) of the simulation was monitored and the simulation reset if certain criterion depending on $N_{eff}$ were met; several reset criterion were employed in order to determine if there was any dependence of the properties estimates on the effective ensemble size, reflecting a bias. No evidence of a systematic dependence of the simulated physical properties on the effective ensemble size was found. Therefore we conclude that there is no evidence that the algorithm of East {\em et al.} and Langfelder {\em et al.} suffers from the bias problem exhibited in similar pure-diffusion quantum Monte Carlo simulations. The results of the simulation (all in atomic units) are as follows: $E_L=-14.6676(7)$, $r=5.96(2)$, $r_2=16.1(1)$, $1/r=8.35(1)$, $1/r^2=53.1(2)$, and $\alpha=38.2(9)$. These are compared to other determinants in the literature.}, note={Supervised by S.M. Rothstein} }

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