RooNDKeysPdf and reflection of correlation coefficients

In the documentation for RooNDKeysPdf it is stated, that the multi-dimensional kernel-estimation ensures “The kernels are constructed such that they reflect the correlation coefficients between the observables in the input dataset.” but I can’t seem to find any further documentation for this. In the note: documenting the underlying algorithms the problem is mentioned but, perhaps due to lack of understanding, I cannot see how this is done still.

I’m currently using RooNDKeysPdf to model distributions for a Mutual Information measure of non-linear correlation in ATLAS data and need to know how the correlations are handled for this. Any help to my ignorance or to the lack of documentation will be most appreciated!


first of all the covariance matrix from the data set is computed, for example as described in … covariance

Then afterwards the data are rotated using the eigenvectors of the matrix and independent gaussian kernels are applied in each dimension of the transformed data.

Best Regards