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Hi Michael, You can also have a look at the new doc PR: j De : users-boun...@openturns.org <users-boun...@openturns.org> de la part de BAUDIN Michael <michael.bau...@edf.fr>
Envoyé : vendredi 10 août 2018 14:22:53 À : users@openturns.org Objet : [ot-users] Confidence bounds of kriging Hi ! I am currently working on kriging and try to reproduce the graphics which is printed in the carrousel of openturns.org : More precisely, I would like to compute the 95% confidence bounds of the kriging predictions. However, I could not find the Python script corresponding to the figure neither on openturns.org nor in the doc (nor in the
Slides of the User’s days, nor in the Use Cases Guide). Is this Python script available ? I also tried to produce the script by myself, and failed.... In PS, I put a Python script which tries to reproduce the figure. The confidence bounds produced by the script are extremely tight compared to what I expected.
My guess is that the issue is related to the estimate of the covariance model : in OpenTURNS, the SquaredExponential is anisotropic while the figure might be produced with an isotropic covariance. I also tried to prevent the optimization algorithm from tuning
the theta parameter with the setOptimizeParameters method, but I wasn’t able to use correctly (the parameters still change, however with a different value). What is the explanation for these tight bounds ? Best regards, Michaël PS # coding: utf-8 #
# # Références #
# Metamodeling with Gaussian processes, Bertrand Iooss, EDF R&D, 2014, www.gdr-mascotnum.fr/media/sssamo14_iooss.pdf # import numpy as np import openturns as ot import pylab as pl # n_test = 100 x_test_coord = np.linspace(0,12,n_test) x_test = ot.Sample(x_test_coord,1) y_test = np.sin(x_test) # Base d'apprentissage de 7 points. # x_train_coord = [1.,3.,4.,6.,7.9,11., 11.5] x_train = ot.Sample(x_train_coord,1) y_train = np.sin(x_train) n_train = len(x_train) n_train # dimension = 1 basis = ot.ConstantBasisFactory(dimension).build() covarianceModel = ot.SquaredExponential([1.]*dimension, [5.0]) algo = ot.KrigingAlgorithm(x_train, y_train, covarianceModel, basis) algo.setOptimizeParameters(False) algo.run() result = algo.getResult() krigeageMM = result.getMetaModel() # krigeageMM = result.getMetaModel() y_test_MM = krigeageMM(x_test) # level = 0.95 alpha = (1-level)/2 sampleQinf = ot.Sample(n_test,1) sampleQsup = ot.Sample(n_test,1) for i in range(n_test): xi = x_test[i] var = result.getConditionalCovariance(xi)[0,0] yi = y_test_MM[i][0]
N = ot.Normal(yi,np.sqrt(var)) q025 = N.computeQuantile(alpha)[0] sampleQinf[i,0] = q025 q975 = N.computeQuantile(1-alpha)[0]
sampleQsup[i,0] = q975 # pl.plot(x_test,y_test,"k-",label="Exact") pl.plot(x_test,y_test_MM,"b--",label="Krigeage") pl.plot(x_train,y_train,"ro",label="Apprentissage") pl.plot(x_test,sampleQinf,"g-",label="%.2f%%" % (100*level)) pl.plot(x_test,sampleQsup,"g-") pl.title("sin") pl.xlabel("X") pl.ylabel("Y") pl.legend()
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