# SubsetSampling¶

class SubsetSampling(*args)

Subset simulation.

Parameters: event : Event Event we are computing the probability of. proposalRange : float, optional Proposal range length targetProbability : float, optional Value of between successive steps

Notes

The goal is to estimate the following probability

The idea of the subset simulation method [Au2001] is to replace simulating a rare failure event in the original probability space by a sequence of simulations of more frequent conditional events

The original probability estimate rewrites

And each conditional subset failure region is chosen by setting the threshold so that leads to a conditional failure probability of order

The conditional samples are generated by the means of Markov Chains, using the Metropolis Hastings algorithm.

being the number of simulations per subset, and the conditional probability of each subset event, and the autocorrelation between Markov chain samples.

The first event not being conditional, expresses as the classic Monte Carlo c.o.v.

Methods

 drawProbabilityConvergence(*args) Draw the probability convergence at a given level. getBlockSize() Accessor to the block size. getClassName() Accessor to the object’s name. getCoefficientOfVariationPerStep() Coefficient of variation per step accessor. getConditionalProbability() Conditional probability accessor. getConvergenceStrategy() Accessor to the convergence strategy. getEvent() Accessor to the event. getEventInputSample() Input sample accessor. getEventOutputSample() Output sample accessor. getGammaPerStep() Autocorrelation accessor. getId() Accessor to the object’s id. getMaximumCoefficientOfVariation() Accessor to the maximum coefficient of variation. getMaximumOuterSampling() Accessor to the maximum sample size. getMaximumStandardDeviation() Accessor to the maximum standard deviation. getName() Accessor to the object’s name. getNumberOfSteps() Subset steps number accesor. getProbabilityEstimatePerStep() Probability estimate accessor. getProposalRange() Proposal range length accessor. getResult() Accessor to the results. getShadowedId() Accessor to the object’s shadowed id. getThresholdPerStep() Threshold accessor. getVerbose() Accessor to verbosity. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. run() Launch simulation. setBetaMin(betaMin) Hypersphere radius accessor. setBlockSize(blockSize) Accessor to the block size. setConditionalProbability(conditionalProbability) Conditional probability accessor. setConvergenceStrategy(convergenceStrategy) Accessor to the convergence strategy. setISubset(iSubset) Conditonal simulation flag accessor. setKeepEventSample(keepEventSample) Sample storage accessor. setMaximumCoefficientOfVariation(…) Accessor to the maximum coefficient of variation. setMaximumOuterSampling(maximumOuterSampling) Accessor to the maximum sample size. setMaximumStandardDeviation(…) Accessor to the maximum standard deviation. setName(name) Accessor to the object’s name. setProgressCallback(*args) Set up a progress callback. setProposalRange(proposalRange) Proposal range length accessor. setShadowedId(id) Accessor to the object’s shadowed id. setStopCallback(*args) Set up a stop callback. setVerbose(verbose) Accessor to verbosity. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

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

drawProbabilityConvergence(*args)

Draw the probability convergence at a given level.

Parameters: level : float, optional The probability convergence is drawn at this given confidence length level. By default level is 0.95. graph : probability convergence graph
getBlockSize()

Accessor to the block size.

Returns: blockSize : int Number of terms in the probability simulation estimator grouped together. It is set by default to 1.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getCoefficientOfVariationPerStep()

Coefficient of variation per step accessor.

Returns: coef : ~openturns.Point Coefficient of variation at each subset step.
getConditionalProbability()

Conditional probability accessor.

Value of between successive steps.

Returns: prob : float Conditional probability value.
getConvergenceStrategy()

Accessor to the convergence strategy.

Returns: storage_strategy : HistoryStrategy Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.
getEvent()

Accessor to the event.

Returns: event : Event Event we want to evaluate the probability.
getEventInputSample()

Input sample accessor.

Returns: inputSample : ~openturns.Sample Input sample.
getEventOutputSample()

Output sample accessor.

Returns: outputSample : ~openturns.Sample Ouput sample.
getGammaPerStep()

Autocorrelation accessor.

Returns: prob : ~openturns.Point Autocorrelation values.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getMaximumCoefficientOfVariation()

Accessor to the maximum coefficient of variation.

Returns: coefficient : float Maximum coefficient of variation of the simulated sample.
getMaximumOuterSampling()

Accessor to the maximum sample size.

Returns: outerSampling : int Maximum number of groups of terms in the probability simulation estimator.
getMaximumStandardDeviation()

Accessor to the maximum standard deviation.

Returns: sigma : float, Maximum standard deviation of the estimator.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getNumberOfSteps()

Subset steps number accesor.

Returns: n : int Number of subset steps.
getProbabilityEstimatePerStep()

Probability estimate accessor.

Returns: prob : ~openturns.Point Probability estimate values.
getProposalRange()

Proposal range length accessor.

Returns: range : float Range length.
getResult()

Accessor to the results.

Returns: results : SimulationResult Structure containing all the results obtained after simulation and created by the method run().
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getThresholdPerStep()

Threshold accessor.

Returns: threshold : ~openturns.Point Threshold values.
getVerbose()

Accessor to verbosity.

Returns: verbosity_enabled : bool If True, the computation is verbose. By default it is verbose.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
run()

Launch simulation.

Notes

It launches the simulation and creates a SimulationResult, structure containing all the results obtained after simulation. It computes the probability of occurence of the given event by computing the empirical mean of a sample of size at most outerSampling * blockSize, this sample being built by blocks of size blockSize. It allows to use efficiently the distribution of the computation as well as it allows to deal with a sample size by a combination of blockSize and outerSampling.

setBetaMin(betaMin)

Parameters: beta : float Radius value of the exclusion hypershere when the conditional simulation is enabled.
setBlockSize(blockSize)

Accessor to the block size.

Parameters: blockSize : int, Number of terms in the probability simulation estimator grouped together. It is set by default to 1.

Notes

For Monte Carlo, LHS and Importance Sampling methods, this allows to save space while allowing multithreading, when available we recommend to use the number of available CPUs; for the Directional Sampling, we recommend to set it to 1.

setConditionalProbability(conditionalProbability)

Conditional probability accessor.

Value of between successive steps.

Parameters: prob : float Conditional probability value.
setConvergenceStrategy(convergenceStrategy)

Accessor to the convergence strategy.

Parameters: storage_strategy : HistoryStrategy Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.
setISubset(iSubset)

Conditonal simulation flag accessor.

Parameters: isubset : bool Whether to enable conditional simulation for the first step of the simulation.
setKeepEventSample(keepEventSample)

Sample storage accessor.

Parameters: prob : bool Whether to keep the event samples.
setMaximumCoefficientOfVariation(maximumCoefficientOfVariation)

Accessor to the maximum coefficient of variation.

Parameters: coefficient : float Maximum coefficient of variation of the simulated sample.
setMaximumOuterSampling(maximumOuterSampling)

Accessor to the maximum sample size.

Parameters: outerSampling : int Maximum number of groups of terms in the probability simulation estimator.
setMaximumStandardDeviation(maximumStandardDeviation)

Accessor to the maximum standard deviation.

Parameters: sigma : float, Maximum standard deviation of the estimator.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setProgressCallback(*args)

Set up a progress callback.

Parameters: callback : callable Takes a float as argument as percentage of progress.
setProposalRange(proposalRange)

Proposal range length accessor.

Parameters: range : float Range length.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setStopCallback(*args)

Set up a stop callback.

Parameters: callback : callable Returns an int deciding whether to stop or continue.
setVerbose(verbose)

Accessor to verbosity.

Parameters: verbosity_enabled : bool If True, make the computation verbose. By default it is verbose.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.