gemseo / uncertainty / sensitivity / morris

# oat module¶

Class to apply the OAT technique used by MorrisIndices.

## OAT technique¶

The purpose of the One-At-a-Time (OAT) methodology is to quantify the elementary effect

$df_i = f(X_1+dX_1,\ldots,X_{i-1}+dX_{i-1},X_i+dX_i,\ldots,X_d) - f(X_1+dX_1,\ldots,X_{i-1}+dX_{i-1},X_i,\ldots,X_d)$

associated with a small variation $$dX_i$$ of $$X_i$$ with

$df_1 = f(X_1+dX_1,\ldots,X_d)-f(X_1,\ldots,X_d)$

The elementary effects $$df_1,\ldots,df_d$$ are computed sequentially from an initial point

$X=(X_1,\ldots,X_d)$

From these elementary effects, we can compare their absolute values $$|df_1|,\ldots,|df_d|$$ and sort $$X_1,\ldots,X_d$$ accordingly.