.. _method-gpais:

"""""
gpais
"""""


Gaussian Process Adaptive Importance Sampling



**Topics**


uncertainty_quantification


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

   method-gpais-build_samples
   method-gpais-seed
   method-gpais-samples_on_emulator
   method-gpais-import_build_points_file
   method-gpais-export_approx_points_file
   method-gpais-max_iterations
   method-gpais-response_levels
   method-gpais-probability_levels
   method-gpais-gen_reliability_levels
   method-gpais-distribution
   method-gpais-rng
   method-gpais-model_pointer


**Specification**

- *Alias:* gaussian_process_adaptive_importance_sampling 

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+-------------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword                | Dakota Keyword Description                    |
|                         | Group              |                               |                                               |
+=========================+====================+===============================+===============================================+
| Optional                                     | `build_samples`__             | Number of initial model evaluations used in   |
|                                              |                               | build phase                                   |
+----------------------------------------------+-------------------------------+-----------------------------------------------+
| Optional                                     | `seed`__                      | Seed of the random number generator           |
+----------------------------------------------+-------------------------------+-----------------------------------------------+
| Optional                                     | `samples_on_emulator`__       | Number of samples at which to evaluate an     |
|                                              |                               | emulator (surrogate)                          |
+----------------------------------------------+-------------------------------+-----------------------------------------------+
| Optional                                     | `import_build_points_file`__  | File containing points you wish to use to     |
|                                              |                               | build a surrogate                             |
+----------------------------------------------+-------------------------------+-----------------------------------------------+
| Optional                                     | `export_approx_points_file`__ | Output file for surrogate model value         |
|                                              |                               | evaluations                                   |
+----------------------------------------------+-------------------------------+-----------------------------------------------+
| Optional                                     | `max_iterations`__            | Number of iterations allowed for optimizers   |
|                                              |                               | and adaptive UQ methods                       |
+----------------------------------------------+-------------------------------+-----------------------------------------------+
| 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-gpais-build_samples.html
__ method-gpais-seed.html
__ method-gpais-samples_on_emulator.html
__ method-gpais-import_build_points_file.html
__ method-gpais-export_approx_points_file.html
__ method-gpais-max_iterations.html
__ method-gpais-response_levels.html
__ method-gpais-probability_levels.html
__ method-gpais-gen_reliability_levels.html
__ method-gpais-distribution.html
__ method-gpais-rng.html
__ method-gpais-model_pointer.html



**Description**


``gpais`` is recommended for problems that have a relatively small
number of input variables (e.g. less than 10-20). This method, Gaussian
Process Adaptive Importance Sampling,
is outlined in the paper :cite:p:`Dalbey2014`.

This method starts with an initial set of LHS samples and adds samples
one at a time, with the goal of adaptively improving the estimate of
the ideal importance density during the process. The approach uses a
mixture of component densities. An iterative process is used
to construct the sequence of improving component densities. At each
iteration, a Gaussian process (GP) surrogate is used to help identify areas
in the space where failure is likely to occur. The GPs are not used to
directly calculate the failure probability; they are only used to approximate
the importance density. Thus, the Gaussian process adaptive importance
sampling algorithm overcomes limitations involving using a potentially
inaccurate surrogate model directly in importance sampling calculations.


