Create a Bayes distribution

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

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

from __future__ import print_function
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()

Out:

/home/devel/project/build/python/src/site-packages/openturns/viewer.py:440: UserWarning: No contour levels were found within the data range.
  contourset = self._ax[0].contour(X, Y, Z, **contour_kw)