estimator_rate

Rate of convergence of mean estimator within multilevel polynomial chaos

Specification

  • Alias: None

  • Arguments: REAL

  • Default: 2

Description

Multilevel Monte Carlo performs optimal resource allocation based on a known estimator variance for the mean statistic:

\[Var[\hat{Q}] = \frac{\sigma^2_Q}{N}\]

Replacing the simple ensemble average estimator in Monte Carlo with a polynomial chaos estimator results in a different and unknown relationship between the estimator variance and the number of samples. In one approach to multilevel PCE, we can employ a parameterized estimator variance:

\[Var[\hat{Q}] = \frac{\sigma^2_Q}{\gamma N^\kappa}\]

for free parameters \(\gamma\) and \(\kappa\) .

The default values are \(\gamma = 1\) and \(\kappa = 2\) (adopts a more aggressive sample profile by assuming a faster convergence rate than Monte Carlo). This advanced specification option allows to user to specify \(\kappa\) , overriding the default.