ImportanceSamplingExperiment

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

Importance Sampling experiment.

Available constructors:

ImportanceSamplingExperiment(distribution)

ImportanceSamplingExperiment(distribution, size)

ImportanceSamplingExperiment(distribution, importanceDistribution, size)

Parameters
distributionDistribution

Distribution \mu with an independent copula used to generate the set of input data.

sizepositive int

Number cardI of points that will be generated in the experiment.

importanceDistributionDistribution

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

See also

WeightedExperiment

Notes

ImportanceSamplingExperiment is a random weighted design of experiments. The generate() method generates points (\Xi_i)_{i \in I} independently from the distribution \mu. When the generate() method is recalled, the generated sample changes. The weights associated to the points are all equal to: \frac{1}{\Xi_i}\frac{\mu(\Xi_i)}{p(\Xi_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(self)

Generate points according to the type of the experiment.

generateWithWeights(self)

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

getClassName(self)

Accessor to the object’s name.

getDistribution(self)

Accessor to the distribution.

getId(self)

Accessor to the object’s id.

getName(self)

Accessor to the object’s name.

getShadowedId(self)

Accessor to the object’s shadowed id.

getSize(self)

Accessor to the size of the generated sample.

getVisibility(self)

Accessor to the object’s visibility state.

hasName(self)

Test if the object is named.

hasUniformWeights(self)

Ask whether the experiment has uniform weights.

hasVisibleName(self)

Test if the object has a distinguishable name.

setDistribution(self, distribution)

Accessor to the distribution.

setName(self, name)

Accessor to the object’s name.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

setSize(self, size)

Accessor to the size of the generated sample.

setVisibility(self, visible)

Accessor to the object’s visibility state.

getImportanceDistribution
__init__(self, \*args)

Initialize self. See help(type(self)) for accurate signature.

generate(self)

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(self)

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(self)

Accessor to the object’s name.

Returns
class_namestr

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

getDistribution(self)

Accessor to the distribution.

Returns
distributionDistribution

Distribution used to generate the set of input data.

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getSize(self)

Accessor to the size of the generated sample.

Returns
sizepositive int

Number cardI of points constituting the design of experiments.

getVisibility(self)

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName(self)

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasUniformWeights(self)

Ask whether the experiment has uniform weights.

Returns
hasUniformWeightsbool

Whether the experiment has uniform weights.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

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

setDistribution(self, distribution)

Accessor to the distribution.

Parameters
distributionDistribution

Distribution used to generate the set of input data.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setSize(self, size)

Accessor to the size of the generated sample.

Parameters
sizepositive int

Number cardI of points constituting the design of experiments.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.