oat module¶
Class to apply the OAT technique used by MorrisIndices
.
OAT technique¶
The purpose of the OneAtaTime (OAT) methodology is to quantify the elementary effect
\[df_i = f(X_1+dX_1,\ldots,X_{i1}+dX_{i1},X_i+dX_i,\ldots,X_d)

f(X_1+dX_1,\ldots,X_{i1}+dX_{i1},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.