@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}
}