Hello Julien,
I appreciate that you try to help me reach my underlying objective.
Still I am not interested in ANCOVA proposed by Caniou (despite some
advantages it has), rather in a Rosenblatt transformation of dependent
variables into independent uniform ones in order to conduct then a PCE
so that one immediately receives mean and variance of the target model.
That's why I wonder how the in Openturns implemented Rosenblatt
transformation works, e. g. is it implemented only for some
distinctive known probabilities or uses it some kind of a kde obtained
from a arbitrary sample set.
Regards,
Simon
Quoting Julien Schueller | Phimeca <[email protected]>:
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ANCOVA is definitely what you are looking for, read again.
If you use a PCE with the correlated data you'll get a correct sobol
decomposition in the decorrelated input spaces through the
iso-probabilistic transformation unfortunately these indices wont mean
anything in terms of the actual original variables.
j
-------------------------
DE : Simon Rittel <[email protected]>
ENVOYé : lundi 17 juin 2019 16:23:31
À : Julien Schueller | Phimeca
CC : [email protected]
OBJET : Re: [ot-users] reply: usage of
Hello Julien,
thank you for your reply.
I should have mentioned in first place that I have read the paper on
ANCOVA based on PCE. As far as I understood one neglects there the
(necessary) assumption of independency of the input vectors in the PCE.
I am rather interested in an approach where you define a specific
ordering of the variables and make them independent. Can you provide
me a short example how the implemented Rosenblatt transformation is
supposed to work? Does it only worked the way it is implemented for
some known distributions or incorporates it a kernel density
estimation of a arbitrary data set?
Thank you,
Simon
PS: Sorry for the fragmentary subject
Quoting Julien Schueller | Phimeca <[email protected]>:
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Hello Simon,
Please have a look at the ANCOVA algorithm.
Julien
-------------------------
DE : [email protected] <[email protected]> de la part
de Simon Rittel <[email protected]>
ENVOYé : jeudi 13 juin 2019 17:23:28
À : [email protected]
OBJET : [ot-users] reply: usage of
Hello,
with one of the four implemented "SobolIndicesAlgorithm"s one can
compute the Sobol coefficients for a function with independent inputs.
Am I correct that there's no direct method implemented to calculate
these coefficients for dependent input variables?
To cope with dependent inputs one could apply the well-known
Rosenblatt transformation before the sensitivity analysis. I saw that
there are already isoprobabilistic transformations implemented, but
from the documentation I couldn't figure out how exactly they are
meant to work (the theory, however, I do understand) and therefore
also how to use them. Maybe you could provide me a short example or
explain briefly how to generate a independent input vector with the
help of the implemented Rosenblatt transformation?
I would appreciate your help on these two questions.
Thank you,
Simon Rittel
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