1Blurb:: Stopping criterion based on relative error
2
3Description:: Multilevel sampling seeks an error balance between the
4estimator variance and the remaining bias error at the highest level,
5the two contributors to mean squared error (MSE).  Since the remaining
6bias error is generally unknown, the convergence_tolerance is used to
7provide a error target relative to the Multifidelity Monte Carlo estimator variance
8resulting from the pilot sample. If the pilot samples are not shaped for the
9low-fidelity model, i.e. the number of low-fidelity evaluations is equal to the
10number of high-fidelity evaluations for each level, the Multifidelity estimator
11falls back to a Multilevel Monte Carlo estimator which is used to assess the
12estimator pilot samples variance.
13The samples allocated at each level are proportional to \f$\frac{1}{\epsilon^2}\f$,
14so each order of magnitude reduction in convergence_tolerance will tend to increase the
15sample allocation by two orders of magnitude.  Therefore, this control
16should be used with care to avoid allocation of huge sample sets that
17could overrun available memory.
18
19<b> Default Behavior </b>
20
21The default value for convergence_tolerance is currently .0001, which
22may be too resolved for expensive simulations or high variance QoI.
23
24
25Topics::
26Examples::
27Theory::
28Faq::
29See_Also::
30