/usr/include/openturns/swig/SubsetSampling_doc.i is in libopenturns-dev 1.9-5.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 | %feature("docstring") OT::SubsetSampling
"Subset simulation.
Parameters
----------
event : :class:`~openturns.Event`
Event we are computing the probability of.
proposalRange : float, optional
Proposal range length
targetProbability : float, optional
Value of :math:`P(F_i|F_{i-1})` between successive steps
Notes
-----
The goal is to estimate the following probability
.. math::
P_f = \\\\int_{\\\\mathcal D_f} f_{\\\\uX}(\\\\ux)\\\\di{\\\\ux}\\\\\\\\
= \\\\int_{\\\\mathbb R^{n_X}} \\\\mathbf{1}_{\\\\{g(\\\\ux,\\\\underline{d}) \\\\:\\\\leq 0\\\\: \\\\}}f_{\\\\uX}(\\\\ux)\\\\di{\\\\ux}\\\\\\\\
= \\\\Prob {\\\\{g(\\\\uX,\\\\underline{d}) \\\\leq 0\\\\}}
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 :math:`F_i`
.. math::
F_1 \\\\supset F_2 \\\\supset \\\\dots \\\\supset F_m = F
The original probability estimate rewrites
.. math::
P_f = P(F_m) = P(\\\\bigcap \\\\limits_{i=1}^m F_i) = P(F_1) \\\\prod_{i=2}^m P(F_i|F_{i-1})
And each conditional subset failure region is chosen by setting the threshold
:math:`g_i` so that :math:`P(F_i|F_{i-1})` leads to a conditional failure
probability of order :math:`0.1`
.. math::
F_i =\\\\Prob {\\\\{g(\\\\uX,\\\\underline{d}) \\\\leq g_i\\\\}}
The conditional samples are generated by the means of Markov Chains,
using the Metropolis Hastings algorithm.
:math:`N` being the number of simulations per subset, and :math:`p_{0i}` the
conditional probability of each subset event, and :math:`\\\\gamma_i` the
autocorrelation between Markov chain samples.
.. math::
\\\\delta^2 = \\\\sum_{i=1}^m \\\\delta^2_i = \\\\sum_{i=1}^m (1+\\\\gamma_i) \\\\frac{1-p_{0i}}{p_{0i}N}
The first event :math:`F_1` not being conditional, :math:`\\\\delta^2_1`
expresses as the classic Monte Carlo c.o.v.
See also
--------
Simulation"
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getCoefficientOfVariationPerStep
"Coefficient of variation per step accessor.
Returns
-------
coef : `~openturns.Point`
Coefficient of variation at each subset step."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::setConditionalProbability
"Conditional probability accessor.
Value of :math:`P(F_i|F_{i-1})` between successive steps.
Parameters
----------
prob : float
Conditional probability value."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getConditionalProbability
"Conditional probability accessor.
Value of :math:`P(F_i|F_{i-1})` between successive steps.
Returns
-------
prob : float
Conditional probability value."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::setKeepEventSample
"Sample storage accessor.
Parameters
----------
prob : bool
Whether to keep the event samples."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getEventInputSample
"Input sample accessor.
Returns
-------
inputSample : `~openturns.Sample`
Input sample."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getEventOutputSample
"Output sample accessor.
Returns
-------
outputSample : `~openturns.Sample`
Ouput sample."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getThresholdPerStep
"Threshold accessor.
Returns
-------
threshold : `~openturns.Point`
Threshold values."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getGammaPerStep
"Autocorrelation accessor.
Returns
-------
prob : `~openturns.Point`
Autocorrelation values."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getProbabilityEstimatePerStep
"Probability estimate accessor.
Returns
-------
prob : `~openturns.Point`
Probability estimate values."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getNumberOfSteps
"Subset steps number accesor.
Returns
-------
n : int
Number of subset steps."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::setProposalRange
"Proposal range length accessor.
Parameters
----------
range : float
Range length."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::getProposalRange
"Proposal range length accessor.
Returns
-------
range : float
Range length."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::setBetaMin
"Hypersphere radius accessor.
Parameters
----------
beta : float
Radius value of the exclusion hypershere when the conditional simulation
is enabled."
// ---------------------------------------------------------------------------
%feature("docstring") OT::SubsetSampling::setISubset
"Conditonal simulation flag accessor.
Parameters
----------
isubset : bool
Whether to enable conditional simulation for the first step of the
simulation."
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