HSICEstimatorGlobalSensitivity

class HSICEstimatorGlobalSensitivity(*args)

Implement a HSIC estimator for global analysis.

Parameters:
covarianceModelCollectionlist of CovarianceModel

List of all covariance kernels. The d first kernels are linked to the input and the last one is for the output.

X2-d sequence of float

The input sample used for the HSIC analysis of dimension d.

Y2-d sequence of float

The output sample used for the HSIC analysis of dimension 1.

estimatorTypeHSICStat

An estimator for internal computations.

See also

HSICEstimatorConditionalSensitivity, HSICEstimatorTargetSensitivity

Examples

>>> import openturns as ot
>>> from math import pi
>>> ot.RandomGenerator.SetSeed(0)

Generate input and output samples.

>>> # 3d input distribution with an independent copula
>>> distX = ot.JointDistribution([ot.Uniform(-pi, pi)] * 3)
>>> X = distX.getSample(100) # get a sample
>>>
>>> # Apply the Ishigami model.
>>> inputs = ['X1', 'X2', 'X3']
>>> formula = ['sin(X1) + 5.0 * (sin(X2))^2 + 0.1 * X3^4 * sin(X1)']
>>> modelIshigami = ot.SymbolicFunction(inputs, formula)
>>> Y = modelIshigami(X) # Y = modelIshigami(X)

Define covariance kernels for the model inputs. Put them in a list.

>>> covarianceModelCollection = []
>>> for i in range(3):
...     Xi = X.getMarginal(i)
...     Cov = ot.SquaredExponential(1)
...     Cov.setScale(Xi.computeStandardDeviation())
...     covarianceModelCollection.append(Cov)

Append the list with the covariance kernel for the model output.

>>> covarianceModelCollection.append(ot.SquaredExponential(Y.computeStandardDeviation()))

Choose the statistic that will be used to estimate the HSIC indices.

>>> estimatorType = ot.HSICUStat() # could be HSICVStat instead

Build and use the HSIC estimator for global sensitivity analysis.

>>> hsic = ot.HSICEstimatorGlobalSensitivity(covarianceModelCollection, X, Y, estimatorType)
>>> print(hsic.getR2HSICIndices())
[0.298073,0.00344498,0.0772657]

Methods

drawHSICIndices()

Draw the HSIC indices.

drawPValuesAsymptotic()

Draw the p-values obtained with an asymptotic formula.

drawPValuesPermutation()

Draw the p-values obtained by permutation.

drawR2HSICIndices()

Draw the R2-HSIC indices.

getClassName()

Accessor to the object's name.

getCovarianceModelCollection()

Get the list of all covariance models used.

getDimension()

Get the dimension of the input sample.

getEstimator()

Get the estimator used for computations.

getHSICIndices()

Get the HSIC indices.

getInputSample()

Get the input sample.

getName()

Accessor to the object's name.

getOutputSample()

Get the output sample.

getPValuesAsymptotic()

Get the p-values obtained with an asymptotic formula.

getPValuesPermutation()

Get the p-value estimated through permutations.

getPermutationSize()

Get the number of permutations.

getR2HSICIndices()

Get the R2-HSIC indices.

getSize()

Get the size of the input sample.

hasName()

Test if the object is named.

run()

Compute all values at once.

setCovarianceModelCollection(coll)

Set the covariance models.

setInputSample(inputSample)

Set the input sample.

setName(name)

Accessor to the object's name.

setOutputSample(outputSample)

Set the output sample.

setPermutationSize(B)

Set the number of permutations to be used for p-value estimate.
__init__(*args)
drawHSICIndices()

Draw the HSIC indices.

Returns:
graphGraph

The graph of all HSIC indices according to components.

drawPValuesAsymptotic()

Draw the p-values obtained with an asymptotic formula.

Returns:
graphGraph

The graph of all p-values estimated with an asymptotic formula.

drawPValuesPermutation()

Draw the p-values obtained by permutation.

Returns:
graphGraph

The graph of all p-values by permutation according to components.

drawR2HSICIndices()

Draw the R2-HSIC indices.

Returns:
graphGraph

The graph of all R2-HSIC indices according to components.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

The object class name (object.__class__.__name__).

getCovarianceModelCollection()

Get the list of all covariance models used.

Returns:
collCovarianceModelCollection

The list of all covariance models used. The last one is the output covariance model.

getDimension()

Get the dimension of the input sample.

Returns:
dimint

The dimension of the input sample.

getEstimator()

Get the estimator used for computations.

Returns:
estimatorHSICStat

The estimator used for internal computations.

getHSICIndices()

Get the HSIC indices.

Returns:
hsicIndicesPoint

The HSIC indices of all components.

getInputSample()

Get the input sample.

Returns:
inSampleSample

The input sample used for analysis.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOutputSample()

Get the output sample.

Returns:
outSampleSample

The output sample used for analysis.

getPValuesAsymptotic()

Get the p-values obtained with an asymptotic formula.

Returns:
pvalsequence of float

The p-values for all components.

getPValuesPermutation()

Get the p-value estimated through permutations.

Returns:
pvalPoint

The p-values of all components estimated with permutations of the data.

getPermutationSize()

Get the number of permutations.

Returns:
permutationSizeint

The number of permutations.

getR2HSICIndices()

Get the R2-HSIC indices.

Returns:
r2hsicIndicesPoint

The R2-HSIC indices of all components.

getSize()

Get the size of the input sample.

Returns:
sizeint

The size of the input sample.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

run()

Compute all values at once.

setCovarianceModelCollection(coll)

Set the covariance models.

Parameters:
collCovarianceModelCollection

The list of all covariance models.

setInputSample(inputSample)

Set the input sample.

Parameters:
inputSample2-d sequence of float

The input sample to be used.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setOutputSample(outputSample)

Set the output sample.

Parameters:
outputSample2-d sequence of float

The output sample to be used.

setPermutationSize(B)

Set the number of permutations to be used for p-value estimate.

Parameters:
Bint

The number of permutation used for p-value estimates.

Examples using the class

The HSIC sensitivity indices: the Ishigami model

The HSIC sensitivity indices: the Ishigami model

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model