import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.ConditionalDistribution().__class__.__name__ == 'ComposedDistribution'):
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif (ot.ConditionalDistribution().__class__.__name__ ==
'CumulativeDistributionNetwork'):
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
elif (ot.ConditionalDistribution().__class__.__name__ == 'Histogram'):
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.ConditionalDistribution()
dimension = distribution.getDimension()
if dimension <= 2:
if distribution.getDimension() == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
else:
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.ConditionalDistribution().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.ConditionalDistribution(
).__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.ConditionalDistribution().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.ConditionalDistribution()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
# choose the initial state within the prior
initialState = prior.getRealization()
# conditional distribution
conditional = ot.Normal()
# create a metropolis-hastings sampler
sampler = ot.RandomWalkMetropolisHastings(
prior, conditional, data, initialState, proposalColl)
sampler.setVerbose(True)
sampler.setThinning(2)
sampler.setBurnIn(500)
sampler.setCalibrationStrategyPerComponent(calibrationColl)
realization = sampler.getRealization()
sigmay = ot.ConditionalDistribution(
ot.Normal(), prior).getStandardDeviation()[0]
w = size * sigma0 ** 2. / (size * sigma0 ** 2. + sigmay ** 2.0)
print("prior variance= %.12g" % (sigma0 ** 2.))
print(" realization=", realization)
print(" w= %.12g" % w)
# the posterior for mu is analytical
print(" expected posterior ~N( %.12g" % (w * data.computeMean()
[0] + (1. - w) * mu0), ", %.12g" % ((w * sigmay ** 2.0 / size) ** 0.5), ")")
# try to generate a sample
sample = sampler.getSample(50)
print(" obtained posterior ~N( %.12g" % sample.computeMean()[
atoms = [ot.Uniform(0.0, 1.0), ot.Uniform(1.0, 2.0)]
conditioningDistributionCollection.append(ot.ComposedDistribution(atoms))
# Second conditioning distribution: discrete/continuous
atoms = [ot.Binomial(3, 0.5), ot.Uniform(1.0, 2.0)]
#conditioningDistributionCollection.append(ot.ComposedDistribution(atoms))
# Third conditioning distribution: dirac/continuous
atoms = [ot.Dirac(0.0), ot.Uniform(1.0, 2.0)]
conditioningDistributionCollection.append(ot.ComposedDistribution(atoms))
for conditioning in conditioningDistributionCollection:
print("conditioning distribution=", conditioning)
observationsDistribution = ot.Distribution(conditionedDistribution)
observationsDistribution.setParameter(conditioning.getMean())
observations = observationsDistribution.getSample(observationsSize)
distribution = ot.PosteriorDistribution(ot.ConditionalDistribution(conditionedDistribution, conditioning), observations)
dim = distribution.getDimension()
print("Distribution ", distribution)
print("Distribution ", distribution)
print("range=", distribution.getRange())
mean = distribution.getMean()
print("Mean ", mean)
print("Covariance ", distribution.getCovariance())
# Is this distribution an elliptical distribution?
print("Elliptical distribution= ", distribution.isElliptical())
# Has this distribution an elliptical copula?
print("Elliptical copula= ", distribution.hasEllipticalCopula())
# Has this distribution an independent copula?
print("Independent copula= ", distribution.hasIndependentCopula())
import openturns.viewer as viewer from matplotlib import pylab as plt # %% # create the Y distribution YDist = ot.Uniform(-1.0, 1.0) # %% # create Theta=f(y) f = ot.SymbolicFunction(['y'], ['y', '1+y^2']) # %% # create the X|Theta distribution XgivenThetaDist = ot.Uniform() # %% # create the distribution XDist = ot.ConditionalDistribution(XgivenThetaDist, YDist, f) XDist.setDescription(['X|Theta=f(y)']) XDist # %% # Get a sample XDist.getSample(5) # %% # draw PDF graph = XDist.drawPDF() view = viewer.View(graph) plt.show()
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.ConditionalDistribution().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.ConditionalDistribution().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.ConditionalDistribution().__class__.__name__ == 'ComposedDistribution':
copula = ot.IndependentCopula(2)
marginals = [ot.Uniform(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, copula)
elif ot.ConditionalDistribution(
).__class__.__name__ == 'CumulativeDistributionNetwork':
coll = [ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])]
distribution = ot.CumulativeDistributionNetwork(
coll, ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.ConditionalDistribution().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.ConditionalDistribution().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.ConditionalDistribution().__class__.__name__ == 'MaximumDistribution':
coll = [
ot.Uniform(2.5, 3.5),
ot.LogUniform(1.0, 1.2),
ot.Triangular(2.0, 3.0, 4.0)
]
distribution = ot.MaximumDistribution(coll)
elif ot.ConditionalDistribution().__class__.__name__ == 'Multinomial':
atoms = [ot.Uniform(0.0, 1.0), ot.Uniform(1.0, 2.0)]
conditioningDistributionCollection.append(ot.ComposedDistribution(atoms))
# Second conditioning distribution: discrete/continuous
atoms = [ot.Binomial(3, 0.5), ot.Uniform(1.0, 2.0)]
# conditioningDistributionCollection.append(ot.ComposedDistribution(atoms))
# Third conditioning distribution: dirac/continuous
atoms = [ot.Dirac(0.0), ot.Uniform(1.0, 2.0)]
conditioningDistributionCollection.append(ot.ComposedDistribution(atoms))
for conditioning in conditioningDistributionCollection:
print("conditioning distribution=", conditioning)
observationsDistribution = ot.Distribution(conditionedDistribution)
observationsDistribution.setParameter(conditioning.getMean())
observations = observationsDistribution.getSample(observationsSize)
distribution = ot.PosteriorDistribution(
ot.ConditionalDistribution(conditionedDistribution, conditioning),
observations)
dim = distribution.getDimension()
print("Distribution ", distribution)
print("Distribution ", distribution)
print("range=", distribution.getRange())
mean = distribution.getMean()
print("Mean ", mean)
print("Covariance ", distribution.getCovariance())
# Is this distribution an elliptical distribution?
print("Elliptical distribution= ", distribution.isElliptical())
# Has this distribution an elliptical copula?
print("Elliptical copula= ", distribution.hasEllipticalCopula())
# Has this distribution an independent copula?