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:

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

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:

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

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.