Conditional distributions

Conditioning is a way to reduce the dimensionnality of a multivariate distribution.

import openturns as ot
import otbenchmark as otb
import openturns.viewer as otv

Conditional distribution of a three dimensional gaussian distribution

The random variable is (X0, X1, X2).

distribution = ot.Normal(3)

We condition with respect to X1=mu1, i.e. we consider (X0, X1, X2) | X1=2.

conditionalIndices = [1]
conditionalReferencePoint = [2.0]
conditionalDistribution = ot.Distribution(
    otb.ConditionalDistribution(
        distribution, conditionalIndices, conditionalReferencePoint
    )
)

_ = otv.View(conditionalDistribution.drawPDF())

Conditional distribution of a three dimensional mixture

Create a Funky distribution

corr = ot.CorrelationMatrix(3)
corr[0, 1] = 0.2
copula = ot.NormalCopula(corr)
x1 = ot.Normal(-1.0, 1.0)
x2 = ot.Normal(2.0, 1.0)
x3 = ot.Normal(1.0, 1.0)
x_funk = ot.ComposedDistribution([x1, x2, x3], copula)

Create a Punk distribution

x1 = ot.Normal(1.0, 1.0)
x2 = ot.Normal(-2, 1.0)
x3 = ot.Normal(2.0, 1.0)
x_punk = ot.ComposedDistribution([x1, x2, x3], copula)

distribution = ot.Mixture([x_funk, x_punk], [0.5, 1.0])

referencePoint = distribution.getMean()
referencePoint

class=Point name=Unnamed dimension=3 values=[0.333333,-0.666667,1.66667]

conditionalIndices = [1]
conditionalReferencePoint = [-0.5]
conditionalDistribution = ot.Distribution(
    otb.ConditionalDistribution(
        distribution, conditionalIndices, conditionalReferencePoint
    )
)

_ = otv.View(conditionalDistribution.drawPDF())

otv.View.ShowAll()