1Blurb:: Rate of convergence of mean estimator within multilevel polynomial chaos
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3Description::
4Multilevel Monte Carlo performs optimal resource allocation based on a
5known estimator variance for the mean statistic:
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7\f[ Var[\hat{Q}] = \frac{\sigma^2_Q}{N} \f]
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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:
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15\f[ Var[\hat{Q}] = \frac{\sigma^2_Q}{\gamma N^\kappa} \f]
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17for free parameters \f$\gamma\f$ and \f$\kappa\f$.
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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.
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24Topics::
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26Examples::
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28Theory::
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30Faq::
31See_Also::
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