Note

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Create a Bayes distributionΒΆ

In this example we are going to build the distribution of the random vector

( \underline{X}|\underline{\Theta}, \underline{Y})

with X conditioned by the random variable Theta obtained with the random variable Y through a function f

\underline{\Theta}=f(\underline{Y})

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt

ot.Log.Show(ot.Log.NONE)

create the Y distribution

YDist = ot.Uniform(-1.0, 1.0)

create Theta=f(y)

f = ot.SymbolicFunction(["y"], ["y", "1 + y"])

create the X|Theta distribution

XgivenThetaDist = ot.Uniform()

create the distribution

XDist = ot.BayesDistribution(XgivenThetaDist, YDist, f)
XDist.setDescription(["X|Theta=f(y)", "y"])
XDist

BayesDistribution(X, Y with X|Theta~Uniform(Theta), Theta=f(Y), f=[y]->[y,1 + y], Y~Uniform(a = -1, b = 1))



Get a sample

sample = XDist.getSample(100)

draw PDF

graph = XDist.drawPDF()
cloud = ot.Cloud(sample)
cloud.setColor("red")
cloud.setLegend("sample")
graph.add(cloud)
view = viewer.View(graph)
plt.show()
[X|Theta=f(y),y] iso-PDF