Voronoi Stratified Sampling

In this example, the stratified sampling method is employed to generate samples from an exponential distribution using Voronoi stratification.

Import the necessary libraries. Here we import standard libraries such as numpy and matplotlib, but also need to import the TrueStratifiedSampling class from UQpy.sampling.

from UQpy.sampling.stratified_sampling.TrueStratifiedSampling import TrueStratifiedSampling
from UQpy.sampling.stratified_sampling.strata import VoronoiStrata
from UQpy.distributions import Exponential
import matplotlib.pyplot as plt
from scipy.spatial import voronoi_plot_2d

Run TrueStratifiedSampling for 25 samples.

• 2 dimensions

• Five strata in each dimension

• Exponential distribution with location parameter = 1 and scale parameter = 1.

Create a distribution object.

marginals = [Exponential(loc=1., scale=1.), Exponential(loc=1., scale=1.)]

Equal number of samples in each stratum

Create strata object using VoronoiStrata class.

strata_obj = VoronoiStrata(seeds_number=8, dimension=2)
sts_vor_obj = TrueStratifiedSampling(distributions=marginals, strata_object=strata_obj,  random_state=3)

Figure shows the stratification of domain using randomly generated seed points

strata_obj

voronoi_plot_2d(strata_obj.voronoi)
plt.title('Stratified Sample - U(0,1)')
plt.xlim([0, 1])
plt.ylim([0, 1])
plt.show()

Run stratified sampling

sts_vor_obj.run(nsamples_per_stratum=3)

Plot the resulting stratified samples and the boundaries of the strata in the \(U(0,1)\) space.

voronoi_plot_2d(strata_obj.voronoi)
plt.title('Stratified Sample - U(0,1)')
plt.plot(sts_vor_obj.samplesU01[:, 0], sts_vor_obj.samplesU01[:, 1], 'dm')
plt.xlim([0, 1])
plt.ylim([0, 1])
plt.show()

sts_vor_obj.weights

Proportional Sampling

TrueStratifiedSampling class can generate samples proportional to volume of each stratum.

sts_vor_obj1 = TrueStratifiedSampling(distributions=marginals, strata_object=strata_obj, random_state=1)
sts_vor_obj1.run(nsamples=10)

It can be noticed that new sample in each stratum is proportional to volume

print('Volume: ', sts_vor_obj1.strata_object.volume)
print('Number of samples in each stratum: ', sts_vor_obj1.nsamples_per_stratum)


voronoi_plot_2d(strata_obj.voronoi)
plt.title('Stratified Sample - U(0,1)')
plt.plot(sts_vor_obj1.samplesU01[:, 0], sts_vor_obj1.samplesU01[:, 1], 'dm')
plt.xlim([0, 1])
plt.ylim([0, 1])
plt.show()