Note that Eq. 7 assumes 𝐕𝐕 𝐃𝐃 (N D × N D ) is proportional to the data variance-covariance matrix. If noise is uncorrelated across 𝐃𝐃, but not necessarily uniform, then 𝐕𝐕 𝐃𝐃 is a diagonal matrix with elements proportional to the variance of each datum. For example, if datum 𝑖𝑖 is averaged twice as much as datum 𝑘𝑘, then 𝐕𝐕 𝐃𝐃 -𝟏𝟏 𝑖𝑖𝑖𝑖 /𝐕𝐕 𝐃𝐃 -𝟏𝟏 𝑘𝑘𝑘𝑘 = 2/1, and hence, the convenience of referring to 𝐕𝐕 𝐃𝐃 -𝟏𝟏 instead of 𝐕𝐕 𝐃𝐃 . We emphasize that 𝐕𝐕 𝐃𝐃 need only be proportional to the true variance-covariance matrix in Eq. 7 since C(𝐩𝐩) ∝ 𝐕𝐕 𝐃𝐃 -𝟏𝟏 and �𝐉𝐉 T 𝐕𝐕 𝐃𝐃 -𝟏𝟏 𝐉𝐉� -1 ∝ 𝐕𝐕 𝐃𝐃 . If noise is both uncorrelated and uniform across 𝐃𝐃, then 𝐕𝐕 𝐃𝐃 -𝟏𝟏 is the identity matrix.