Blurb::
Formulation for emulation of model discrepancies.

Description:: 
In many uncertainty quantification approaches, model discrepancies are 
emulated using, e.g., polynomial chaos, stochastic collocation, or 
Gaussian process models.  Two formulations are available for this 
emulation: 
<ol>
  <li> \c distinct emulation (default), in which we directly approximate 
       the difference or ratio between the evaluations of two models 
       or solution levels.
  <li> \c recursive emulation (experimental option), in which we 
       approximate a difference or ratio among the new model evaluation 
       and the emulator approximation of the previous model.
</ol>

The latter approach is a form of hierarchical emulation in which we 
emulate the surplus between the previous emulator and the new modeling 
level.  This approach has a few advantages: (i) it reduces bias by
correcting for emulation errors that occur at previous levels, and (ii)
it does not require paired model evaluations for each discrepancy level,
which reduces cost, allows for disparate sample points, and simplifies 
data imports. 
<!-- and (iii) discrepancy emulation supports local error estimation 
     through hierarchical surplus. -->
On the other hand, its primary disadvantage is that the aggregate
emulation is only as good as its weakest link, in that a poor emulator 
recovery can create difficulty in accurately resolving discrepancies 
that are recursively dependent on it.  Thus, the \c distinct approach
may tend to be more expensive in exchange for greater robustness.

Topics::

Examples::
\verbatim
method,
        multilevel_polynomial_chaos
	  expansion_order_sequence = 2
	  collocation_ratio = .9
	  orthogonal_matching_pursuit
	  discrepancy_emulation recursive
\endverbatim

Theory::
Faq::
See_Also::	
