I was reading a stats book that mentioned Mahalanobis distance and that made me think of Non Nobis from Henry V, a great scene in a great movie. As far as I know, there’s no connection between Mahalanobis and Non Nobis except that both end in “nobis.”
Since Mahalanobis is an Indian surname and Non Nobis is Latin, there’s probably no etymological connection between the two except maybe way back in Indo-European.
Mahalanobis distance is Euclidean distance adapted to a multivariate normal distribution. Specifically, the squared distance between two column vectors x and y is
(x – y)T S-1 (x – y)
where S is the covariance matrix for a multivariate Gaussian distribution.
You might look at this and ask why the matrix in the middle has to be the inverse of a covariance matrix. Couldn’t it be any invertible matrix? Isn’t this just Euclidean distance in transformed coordinates? Yes and yes. But Mahalanobis thought of how to use it in statistics.
Mahalanobis’ birthday, June 29, is National Statistics Day in India in his honor.