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
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]>:
> <!-- .EmailQuote { margin-left: 1pt; padding-left: 4pt; border-left:
> #800000 2px solid; } --><!-- p {margin-top:0; margin-bottom:0} -->
> 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
>
> _______________________________________________
> OpenTURNS users mailing list
> [email protected]
> http://openturns.org/mailman/listinfo/users
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]>:
> <!-- .EmailQuote { margin-left: 1pt; padding-left: 4pt; border-left:
> #800000 2px solid; } --><!-- p {margin-top:0; margin-bottom:0} -->
> 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
>
> _______________________________________________
> OpenTURNS users mailing list
> [email protected]
> http://openturns.org/mailman/listinfo/users
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