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Deriving the Optimal Scoring Matrix

Our next goal is to construct a scoring matrix that is optimal to estimate distances. An optimal estimator (scoring function) has the smallest variance. Let d* = SE-1(w/n) be our estimate of the distance using w. To compute the expected value of d* and its variance, we use the Taylor expansion of SE-1(w/n) around SE(d). These computations were done with a computer algebra system (Maple), they are too tedious and error prone to be done by hand.


Chantal Korostensky