# Analyzing 2nd-order Sobol Indices

**URL:** <https://discourse.julialang.org/t/analyzing-2nd-order-sobol-indices/113664>\
**Category:** Modelling & Simulations\
**Created:** [April 30, 2024, 5:17pm UTC](https://discourse.julialang.org/t/analyzing-2nd-order-sobol-indices/113664 "2024-04-30T17:17:55Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Nick1](https://avatars.discourse-cdn.com/v4/letter/n/47e85d/32.png) [@Nick1](https://discourse.julialang.org/u/Nick1)\
**Post date:** [April 30, 2024, 5:17pm UTC](https://discourse.julialang.org/t/analyzing-2nd-order-sobol-indices/113664/1 "2024-04-30T17:17:55Z")

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I have a model with 130 parameters and measure 18 outputs. I ran the Sobol analysis for the 2nd-order indices because there is a significant difference between the total indices and 1st-order, so I guess there are higher-order interactions. The output is a tensor (130, 130, 18). How could I interpret the output? I also observed that each layer is an upper triangular matrix.

Thanks!

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**Author:** ![Vaibhavdixit02](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/vaibhavdixit02/32/2916_2.png) [@Vaibhavdixit02](https://discourse.julialang.org/u/Vaibhavdixit02)\
**Post date:** [May 10, 2024, 3:35am UTC](https://discourse.julialang.org/t/analyzing-2nd-order-sobol-indices/113664/2 "2024-05-10T03:35:18Z")

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So the 130x130 matrix is basically the s\_{ij} i.e. the second order sensitivity wrt to the ith and jth parameters, of each of the output `f(x)[k]`. I hope that clarifies!

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**Author:** ![Nick1](https://avatars.discourse-cdn.com/v4/letter/n/47e85d/32.png) [@Nick1](https://discourse.julialang.org/u/Nick1)\
**Post date:** [May 13, 2024, 5:14pm UTC](https://discourse.julialang.org/t/analyzing-2nd-order-sobol-indices/113664/3 "2024-05-13T17:14:58Z")

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Thank you for the answer! It clarifies it. About the upper triangular matrix, is it problem specific or general way to express the higher-order interactions?