ImportanceSamplingExperiment

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../../_images/ImportanceSamplingExperiment.png
class ImportanceSamplingExperiment(*args)

Importance Sampling experiment.

Available constructors:

ImportanceSamplingExperiment(importanceDistribution)

ImportanceSamplingExperiment(importanceDistribution, size)

ImportanceSamplingExperiment(initialDistribution, importanceDistribution, size)

Parameters:
initialDistributionDistribution

Distribution \mu which is the initial distribution used to generate the set of input data.

sizepositive int

Number of points that will be generated in the experiment.

importanceDistributionDistribution

Distribution p according to which the points of the experiments will be generated with the Importance Sampling technique.

See also

WeightedExperiment

Notes

ImportanceSamplingExperiment is a random weighted design of experiments to get a sample (X_i)_{1 \leq i \leq size} independently according to the distribution \mu. The sample is generated from the importance distribution p and each realization is weighted by \frac{\mu(X_i)}{p(X_i)}

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.ComposedDistribution([ot.Uniform(0, 1)] * 2)
>>> importanceDistribution = ot.ComposedDistribution([ot.Uniform(0, 1)] * 2)
>>> experiment = ot.ImportanceSamplingExperiment(distribution, importanceDistribution, 5)
>>> print(experiment.generate())
    [ X0        X1        ]
0 : [ 0.629877  0.882805  ]
1 : [ 0.135276  0.0325028 ]
2 : [ 0.347057  0.969423  ]
3 : [ 0.92068   0.50304   ]
4 : [ 0.0632061 0.292757  ]

Methods

generate()

Generate points according to the type of the experiment.

generateWithWeights()

Generate points and their associated weight according to the type of the experiment.

getClassName()

Accessor to the object's name.

getDistribution()

Accessor to the distribution.

getId()

Accessor to the object's id.

getName()

Accessor to the object's name.

getShadowedId()

Accessor to the object's shadowed id.

getSize()

Accessor to the size of the generated sample.

getVisibility()

Accessor to the object's visibility state.

hasName()

Test if the object is named.

hasUniformWeights()

Ask whether the experiment has uniform weights.

hasVisibleName()

Test if the object has a distinguishable name.

setDistribution(distribution)

Accessor to the distribution.

setName(name)

Accessor to the object's name.

setShadowedId(id)

Accessor to the object's shadowed id.

setSize(size)

Accessor to the size of the generated sample.

setVisibility(visible)

Accessor to the object's visibility state.

getImportanceDistribution
__init__(*args)
generate()

Generate points according to the type of the experiment.

Returns:
sampleSample

Points (\Xi_i)_{i \in I} which constitute the design of experiments with card I = size. The sampling method is defined by the nature of the weighted experiment.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5)
>>> sample = myExperiment.generate()
>>> print(sample)
    [ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
3 : [ -0.355007  1.43725  ]
4 : [  0.810668  0.793156 ]
generateWithWeights()

Generate points and their associated weight according to the type of the experiment.

Returns:
sampleSample

The points which constitute the design of experiments. The sampling method is defined by the nature of the experiment.

weightsPoint of size cardI

Weights (\omega_i)_{i \in I} associated with the points. By default, all the weights are equal to 1/cardI.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5)
>>> sample, weights = myExperiment.generateWithWeights()
>>> print(sample)
    [ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
3 : [ -0.355007  1.43725  ]
4 : [  0.810668  0.793156 ]
>>> print(weights)
[0.2,0.2,0.2,0.2,0.2]
getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getDistribution()

Accessor to the distribution.

Returns:
distributionDistribution

Distribution used to generate the set of input data.

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

getSize()

Accessor to the size of the generated sample.

Returns:
sizepositive int

Number cardI of points constituting the design of experiments.

getVisibility()

Accessor to the object’s visibility state.

Returns:
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

hasUniformWeights()

Ask whether the experiment has uniform weights.

Returns:
hasUniformWeightsbool

Whether the experiment has uniform weights.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:
hasVisibleNamebool

True if the name is not empty and not the default one.

setDistribution(distribution)

Accessor to the distribution.

Parameters:
distributionDistribution

Distribution used to generate the set of input data.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:
idint

Internal unique identifier.

setSize(size)

Accessor to the size of the generated sample.

Parameters:
sizepositive int

Number cardI of points constituting the design of experiments.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:
visiblebool

Visibility flag.

Examples using the class

Use the Importance Sampling algorithm

Use the Importance Sampling algorithm

Axial stressed beam : comparing different methods to estimate a probability

Axial stressed beam : comparing different methods to estimate a probability