From ee1d892118a4a594a99519afd071497b4275f46c Mon Sep 17 00:00:00 2001 From: Prateek Bhustali Date: Sun, 3 Jul 2022 17:15:06 +0200 Subject: [PATCH] Minor changes in documentation --- docs/source/sensitivity/chatterjee.rst | 3 ++- docs/source/sensitivity/sobol.rst | 2 +- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/docs/source/sensitivity/chatterjee.rst b/docs/source/sensitivity/chatterjee.rst index 57921b4b..42ee716e 100644 --- a/docs/source/sensitivity/chatterjee.rst +++ b/docs/source/sensitivity/chatterjee.rst @@ -9,8 +9,9 @@ Consider :math:`n` samples of random variables :math:`X` and :math:`Y`, with :ma \xi_{n}(X, Y):=1-\frac{3 \sum_{i=1}^{n-1}\left|r_{i+1}-r_{i}\right|}{n^{2}-1} -The Chatterjee index converges for :math:`n \rightarrow \infty` to the Cramér-von Mises index and is faster to estimate than using the Pick and Freeze approach in the Cramér-von Mises index. +The Chatterjee index converges for :math:`n \rightarrow \infty` to the Cramér-von Mises index and is faster to estimate than using the Pick and Freeze approach to compute the the Cramér-von Mises index. +Furthermore, the Sobol indices can be efficiently estimated by leveraging the same rank statistics, which has the advantage that any sample can be used and no specific pick and freeze scheme is required. Chatterjee Class ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ diff --git a/docs/source/sensitivity/sobol.rst b/docs/source/sensitivity/sobol.rst index 60469b28..4b482e81 100644 --- a/docs/source/sensitivity/sobol.rst +++ b/docs/source/sensitivity/sobol.rst @@ -17,7 +17,7 @@ If the first order index of an input parameter is equal to the total order index The Sobol indices are typically computed using the Pick-and-Freeze approach for single output and multi-output models. Since there are several variants of the Pick-and-Freeze approach, the schemes implemented to compute Sobol indices are listed below: -Here, :math:`N` is the number of Monte Carlo samples and :math:`m` being the number of input parameters in the model. +Here, :math:`N` is the Monte Carlo sample size and :math:`m` is the number of input parameters in the model. 1. **First order indices** (:math:`S_{i}`)