Dakota Reference Manual  Version 6.15
Explore and Predict with Confidence
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estimator_rate


Rate of convergence of mean estimator within multilevel polynomial chaos

Specification

Alias: none

Argument(s): 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.