1Blurb:: Rate of convergence of mean estimator within multilevel polynomial chaos 2 3Description:: 4Multilevel Monte Carlo performs optimal resource allocation based on a 5known estimator variance for the mean statistic: 6 7\f[ Var[\hat{Q}] = \frac{\sigma^2_Q}{N} \f] 8 9Replacing the simple ensemble average estimator in Monte Carlo with a 10polynomial chaos estimator results in a different and unknown 11relationship between the estimator variance and the number of samples. 12In one approach to multilevel PCE, we can employ a parameterized 13estimator variance: 14 15\f[ Var[\hat{Q}] = \frac{\sigma^2_Q}{\gamma N^\kappa} \f] 16 17for free parameters \f$\gamma\f$ and \f$\kappa\f$. 18 19The default values are \f$\gamma = 1\f$ and \f$\kappa = 2\f$ (adopts a 20more aggressive sample profile by assuming a faster convergence rate 21than Monte Carlo). This advanced specification option allows to user 22to specify \f$\kappa\f$, overriding the default. 23 24Topics:: 25 26Examples:: 27 28Theory:: 29 30Faq:: 31See_Also:: 32