# Sobol indices based on PCE

**URL:** <https://uqworld.org/t/sobol-indices-based-on-pce/3793>\
**Category:** Community Q&A and How To\
**Tags:** sensitivity, pce\
**Created:** [August 29, 2024, 7:42am UTC](https://uqworld.org/t/sobol-indices-based-on-pce/3793 "2024-08-29T07:42:03Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Mr121Tony](https://uqworld.org/user_avatar/uqworld.org/mr121tony/32/1070_2.png) [@Mr121Tony](https://uqworld.org/u/Mr121Tony)\
**Post date:** [August 29, 2024, 7:42am UTC](https://uqworld.org/t/sobol-indices-based-on-pce/3793/1 "2024-08-29T07:42:03Z")

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Dear Professor,  
I use Sobol indices based on PCE to do sensitivity analysis about a complex structure. There are 20 random input variables. The final LOO error estimate is about 0.18, which is minimized in all tried ExpDesign.  
However, the sum of all the Sobol indices of random input variables is more than 1. Is it right? If it is right, how to explain it?

Best wishes!  
Tony Smith

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**Author:** ![styfen.schaer](https://uqworld.org/user_avatar/uqworld.org/styfen.schaer/32/849_2.png) [@styfen.schaer](https://uqworld.org/u/styfen.schaer)\
**Post date:** [August 29, 2024, 12:30pm UTC](https://uqworld.org/t/sobol-indices-based-on-pce/3793/2 "2024-08-29T12:30:37Z")

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Dear @Mr121Tony ,

I think [this](https://uqworld.org/t/total-sobol-indices-sum-to-more-than-1/915) topic will clarify your question.

Best regards,  
Styfen

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**Author:** ![Mr121Tony](https://uqworld.org/user_avatar/uqworld.org/mr121tony/32/1070_2.png) [@Mr121Tony](https://uqworld.org/u/Mr121Tony)\
**Post date:** [September 9, 2024, 9:06am UTC](https://uqworld.org/t/sobol-indices-based-on-pce/3793/3 "2024-09-09T09:06:56Z")

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Dear @styfen.schaer  
Thank you very much. It helps me a lot.  
Best wishes!  
Tony Smith