.. _method-global_evidence:

"""""""""""""""
global_evidence
"""""""""""""""


Evidence theory with evidence measures computed with global optimization methods



**Topics**


epistemic_uncertainty_quantification_methods, evidence_theory


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

   method-global_evidence-samples
   method-global_evidence-seed
   method-global_evidence-sbgo
   method-global_evidence-ego
   method-global_evidence-ea
   method-global_evidence-lhs
   method-global_evidence-response_levels
   method-global_evidence-probability_levels
   method-global_evidence-gen_reliability_levels
   method-global_evidence-distribution
   method-global_evidence-rng
   method-global_evidence-model_pointer


**Specification**

- *Alias:* nond_global_evidence 

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+----------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword             | Dakota Keyword Description                    |
|                         | Group              |                            |                                               |
+=========================+====================+============================+===============================================+
| Optional                                     | `samples`__                | Number of samples for sampling-based methods  |
+----------------------------------------------+----------------------------+-----------------------------------------------+
| Optional                                     | `seed`__                   | Seed of the random number generator           |
+-------------------------+--------------------+----------------------------+-----------------------------------------------+
| Optional (Choose One)   | Solution Approach  | `sbgo`__                   | Use the surrogate based optimization method   |
|                         |                    +----------------------------+-----------------------------------------------+
|                         |                    | `ego`__                    | Use the Efficient Global Optimization method  |
|                         |                    +----------------------------+-----------------------------------------------+
|                         |                    | `ea`__                     | Use an evolutionary algorithm                 |
|                         |                    +----------------------------+-----------------------------------------------+
|                         |                    | `lhs`__                    | Uses Latin Hypercube Sampling (LHS) to sample |
|                         |                    |                            | variables                                     |
+-------------------------+--------------------+----------------------------+-----------------------------------------------+
| Optional                                     | `response_levels`__        | Values at which to estimate desired           |
|                                              |                            | statistics for each response                  |
+----------------------------------------------+----------------------------+-----------------------------------------------+
| Optional                                     | `probability_levels`__     | Specify probability levels at which to        |
|                                              |                            | estimate the corresponding response value     |
+----------------------------------------------+----------------------------+-----------------------------------------------+
| Optional                                     | `gen_reliability_levels`__ | Specify generalized relability levels at      |
|                                              |                            | which to estimate the corresponding response  |
|                                              |                            | value                                         |
+----------------------------------------------+----------------------------+-----------------------------------------------+
| Optional                                     | `distribution`__           | Selection of cumulative or complementary      |
|                                              |                            | cumulative functions                          |
+----------------------------------------------+----------------------------+-----------------------------------------------+
| Optional                                     | `rng`__                    | Selection of a random number generator        |
+----------------------------------------------+----------------------------+-----------------------------------------------+
| Optional                                     | `model_pointer`__          | Identifier for model block to be used by a    |
|                                              |                            | method                                        |
+----------------------------------------------+----------------------------+-----------------------------------------------+

.. __: method-global_evidence-samples.html
__ method-global_evidence-seed.html
__ method-global_evidence-sbgo.html
__ method-global_evidence-ego.html
__ method-global_evidence-ea.html
__ method-global_evidence-lhs.html
__ method-global_evidence-response_levels.html
__ method-global_evidence-probability_levels.html
__ method-global_evidence-gen_reliability_levels.html
__ method-global_evidence-distribution.html
__ method-global_evidence-rng.html
__ method-global_evidence-model_pointer.html



**Description**


``global_evidence`` allows the user to specify
several global approaches for calculating the belief and plausibility functions:

- ``lhs`` - note: this takes the minimum and maximum of the samples as the bounds per "interval cell combination."
- ``ego`` - uses Efficient Global Optimization which is based on an adaptive Gaussian process surrogate.
- ``sbo`` - uses a Gaussian process surrogate (non-adaptive) within an optimization process.
- ``ea`` - uses an evolutionary algorithm.  This can be expensive as the ea will be run for each interval cell combination.


Note that to calculate the plausibility and belief cumulative
distribution functions, one has to look at all combinations of
intervals for the uncertain variables. In terms of implementation, if
one is using LHS sampling as outlined above, this method creates a
large sample over the response surface, then examines each cell to
determine the minimum and maximum sample values within each cell. To
do this, one needs to set the number of samples relatively high: the
default is 10,000 and we recommend at least that number. If the model
you are running is a simulation that is computationally quite
expensive, we recommend that you set up a surrogate model within the
Dakota input file so that ``global_evidence`` performs its sampling and
calculations on the surrogate and not on the original model. If one
uses optimization methods instead to find the minimum and maximum
sample values within each cell, this can also be computationally
expensive.

*Additional Resources*

See the topic page :ref:`topic-evidence_theory` for important
background information and usage notes.

Refer to :ref:`topic-variable_support` for information on supported
variable types.



**Theory**


The basic idea is that one specifies an "evidence structure"
on uncertain inputs and propagates that to obtain belief and
plausibility functions on the response functions. The inputs are
defined by sets of intervals and Basic Probability Assignments (BPAs).
Evidence propagation is computationally expensive, since the minimum
and maximum function value must be calculated for each "interval cell
combination." These bounds are aggregated into belief and
plausibility.


