.. _method-multilevel_sampling-convergence_tolerance:

"""""""""""""""""""""
convergence_tolerance
"""""""""""""""""""""


Stopping criterion based on relative error


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* REAL

- *Default:* 1.e-4


**Description**


Multilevel sampling seeks an error balance between the
estimator variance and the remaining bias error at the highest level,
the two contributors to mean squared error (MSE).  Since the remaining
bias error is generally unknown, the convergence_tolerance is used to
provide a error target relative to the Multifidelity Monte Carlo estimator variance
resulting from the pilot sample. If the pilot samples are not shaped for the
low-fidelity model, i.e. the number of low-fidelity evaluations is equal to the
number of high-fidelity evaluations for each level, the Multifidelity estimator
falls back to a Multilevel Monte Carlo estimator which is used to assess the
estimator pilot samples variance.
The samples allocated at each level are proportional to :math:`\frac{1}{\epsilon^2}` ,
so each order of magnitude reduction in convergence_tolerance will tend to increase the
sample allocation by two orders of magnitude.  Therefore, this control
should be used with care to avoid allocation of huge sample sets that
could overrun available memory.

*Default Behavior*

The default value for convergence_tolerance is currently .0001, which
may be too resolved for expensive simulations or high variance QoI.


