2.3.3. The MMSE estimator For any rotation distribution Λ and loss function over , the MLE and MAP estimators can be further improved by the corresponding Bayes estimator which minimizes the posterior expected loss . In particular, following the definition (equation 5) of the Bayes estimator, and for the chordal distance dF(·, ·) (equation 9), with its corresponding squared loss , the Bayes estimator takes the form where the expectation is taken over the posterior density (equation 8).
