gemseo.uncertainty package#

Uncertainty quantification and management.

The package uncertainty provides several functionalities to quantify and manage uncertainties. Most of them can be used from the high-level functions provided by this module.

The sub-package distributions offers an abstract level for probability distributions, as well as interfaces to the OpenTURNS and SciPy ones. It is also possible to fit a probability distribution from data or select the most likely one from a list of candidates. These distributions can be used to define random variables in a ParameterSpace before propagating these uncertainties through a system of Discipline, by means of a DOEScenario.

See also

EmpiricalStatistics ParametricStatistics

create_distribution(distribution_name, **options)[source]#

Create a distribution.

Parameters:

distribution_name (str) -- The name of a class implementing a probability distribution, e.g. 'OTUniformDistribution' or 'SPDistribution'.
**options -- The distribution options.

Return type:

BaseDistribution

Examples

>>> from gemseo.uncertainty import create_distribution
>>>
>>> distribution = create_distribution("OTNormalDistribution", mu=1, sigma=2)
>>> print(distribution)
Normal(mu=1, sigma=2)
>>> print(distribution.mean, distribution.standard_deviation)
1.0 2.0
>>> samples = distribution.compute_samples(10)
>>> print(samples.shape)
(10,)

create_sensitivity_analysis(analysis, samples='')[source]#

Create the sensitivity analysis.

Parameters:

analysis (str) -- The name of a sensitivity analysis class.
samples (IODataset | str | Path) --
The samples for the estimation of the sensitivity indices, either as an IODataset or as a pickle file path generated from the IODataset.to_pickle method. If empty, use compute_samples().

By default it is set to "".

Returns:

The sensitivity analysis.

Return type:

BaseSensitivityAnalysis

create_statistics(dataset, variable_names=(), tested_distributions=(), fitting_criterion='', selection_criterion='best', level=0.05, name='')[source]#

Create a toolbox to estimate statistics, either empirically or parametrically.

If parametrically, the toolbox selects a distribution from candidates, based on a goodness-of-fit criterion and on a selection strategy.

Parameters:

dataset (Dataset) -- A dataset.
variable_names (Iterable[str]) --
The names of the variables of interest. If empty, consider all the variables of the dataset.

By default it is set to ().
tested_distributions (Sequence[str]) --
The names of the probability distributions to be used as candidates. Either SciPy class names or OpenTURNS class names. Do not mix SciPy and OpenTURNS class names.

By default it is set to ().
fitting_criterion (str) --
The name of a goodness-of-fit criterion, measuring how a distribution fits the data. If empty, use OTDistributionFitter.default_fitting_criterion` or SPDistributionFitter.default_fitting_criterion` according to the type of tested_distributions.

By default it is set to "".
selection_criterion (str) --
The name of a selection criterion to select a distribution from tested_distributions. Either "first" (select the first distribution satisfying a fitting criterion) or "best" (select the distribution that best satisfies a fitting criterion).

By default it is set to "best".
level (float) --
A test level, i.e. the risk of committing a Type 1 error, that is an incorrect rejection of a true null hypothesis, for criteria based on a test hypothesis.

By default it is set to 0.05.
name (str) --
A name for the statistics toolbox. If empty, concatenate the statistics class name and the dataset name.

By default it is set to "".

Returns:

A statistics toolbox.

Return type:

BaseStatistics

Examples

>>> from gemseo import (
...     create_discipline,
...     create_parameter_space,
...     create_scenario,
... )
>>> from gemseo.uncertainty import create_statistics
>>>
>>> expressions = {"y1": "x1+2*x2", "y2": "x1-3*x2"}
>>> discipline = create_discipline(
...     "AnalyticDiscipline", expressions=expressions
... )
>>>
>>> parameter_space = create_parameter_space()
>>> parameter_space.add_random_variable(
...     "x1", "OTUniformDistribution", minimum=-1, maximum=1
... )
>>> parameter_space.add_random_variable(
...     "x2", "OTNormalDistribution", mu=0.5, sigma=2
... )
>>>
>>> scenario = create_scenario(
...     [discipline],
...     "y1",
...     parameter_space,
...     formulation_name="DisciplinaryOpt",
...     scenario_type="DOE",
... )
>>> scenario.execute(algo_name="OT_MONTE_CARLO", n_samples=100)
>>>
>>> dataset = scenario.to_dataset(opt_naming=False)
>>>
>>> statistics = create_statistics(dataset)
>>> mean = statistics.compute_mean()

get_available_distributions(base_class_name='BaseDistribution')[source]#

Get the available probability distributions.

Parameters:

base_class_name (str) --

The name of the base class of the probability distributions, e.g. "BaseDistribution", "OTDistribution" or "SPDistribution".

By default it is set to "BaseDistribution".

Returns:

The names of the available probability distributions.

Return type:

list[str]

get_available_sensitivity_analyses()[source]#

Get the available sensitivity analyses.

Return type:: list[str]

load_sensitivity_analysis(file_path)[source]#

Load a sensitivity analysis from the disk.

Parameters:: file_path (str | Path) -- The path to the file.
Returns:: The sensitivity analysis.
Return type:: BaseSensitivityAnalysis

gemseo.uncertainty package#

Subpackages#

This Page