Hi ! I have a computer code with dependent input vector and I would like to perform sensitivity analysis on the vector output. To do this, I would like to estimate the Sobol' indices. In order to workaround the dependent inputs, I would like to gather dependent input variables into independent groups and to estimate the Sobol' indices on these groups.
· My first idea is to use a chaos expansion in order to estimate Sobol' indices. It is easy to estimate the first order Sobol' indices with the getSobolGroupedIndex method of the FunctionnalChaosSobolIndices class: http://openturns.github.io/openturns/master/user_manual/response_surface/_generated/openturns.FunctionalChaosSobolIndices.html However, the corresponding total order indices method seem to be unavailable: there is no getSobolGroupedTotalIndex ? If so, this is a pity, since this is just another "simple" arrangement of the coefficients from the chaos expansion. It would allow to estimate the total effect of a group. Compared to the group Sobol first indice, it would allow to see if there are interactions with this group and other variables outside from the group. Also, if the group Sobol total indice is close to zero, this means that this group has no effect of the variability of the output. · The second topic of my post is the SobolIndicesAlgorithm class : http://openturns.github.io/openturns/master/user_manual/_generated/openturns.SobolIndicesAlgorithm.html I can see that there is no "group" method here. Is there a theoretical way of computing grouped Sobol' indices with these estimators? · Finally, I would like to know if there is a way of using the joint distribution in order to generate the independent groups of dependent input variables? In other words, with a given multivariate joint distribution, is there a way of generating a list of sub-lists of indices such that: o Each sub-list contain dependent variables, o Two sub-lists are independent. With such a goal, what classes / methods to use ? Best regards, Michaël PS By the way, the total Sobol' indices of a group of variables lead to a way of removing input variables from the model. Indeed, we could compute the largest group having a total Sobol' indice lower than a given small threshold (says 0.01 for example). By design, all variables from this group could be replaced by fixed inputs without changing the variability of the output. Furthermore, if we had the distribution of this estimator, we could guarantee this property with, say, 95% confidence (i.e. including the variability from the estimate). In order to compute this group, the variables could first be ordered by decreasing total Sobol' indices. Then, we could add the variables into the group until the total Sobol' indice exceeds the threshold: the final group is the one just before this step. With this raw algorithm, the chaos expansion has a great advantage: given that the decomposition is known, the estimate is almost CPU-free. Ce message et toutes les pièces jointes (ci-après le 'Message') sont établis à l'intention exclusive des destinataires et les informations qui y figurent sont strictement confidentielles. Toute utilisation de ce Message non conforme à sa destination, toute diffusion ou toute publication totale ou partielle, est interdite sauf autorisation expresse. Si vous n'êtes pas le destinataire de ce Message, il vous est interdit de le copier, de le faire suivre, de le divulguer ou d'en utiliser tout ou partie. Si vous avez reçu ce Message par erreur, merci de le supprimer de votre système, ainsi que toutes ses copies, et de n'en garder aucune trace sur quelque support que ce soit. Nous vous remercions également d'en avertir immédiatement l'expéditeur par retour du message. Il est impossible de garantir que les communications par messagerie électronique arrivent en temps utile, sont sécurisées ou dénuées de toute erreur ou virus. ____________________________________________________ This message and any attachments (the 'Message') are intended solely for the addressees. The information contained in this Message is confidential. Any use of information contained in this Message not in accord with its purpose, any dissemination or disclosure, either whole or partial, is prohibited except formal approval. If you are not the addressee, you may not copy, forward, disclose or use any part of it. If you have received this message in error, please delete it and all copies from your system and notify the sender immediately by return message. E-mail communication cannot be guaranteed to be timely secure, error or virus-free.
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