In practice the individual experts will not output the true aposteriori
probabilities
but instead their estimates
where
and
is the estimation error. Replacing the aposteriori class probabilities
in the decision rule (
10
) with their hatted counterparts and substituting from (
13
) we have
which can be rewritten as
A comparison of ( 10 ) and ( 15 ) shows that each term in the error free expert combination rule ( 10 ) is affected by error factor
Thus in the weighted average rule the compounded effect of errors, which is computed as a sum, is scaled by the the sum of the weighted aposteriori probabilities. This will result in the dampening of the errors. Thus the weighted sum decision rule can be expected to be resilient to estimation errors and also to approximation errors that we may have inadvertently introduced in developing it. It follows, therefore, that the weighted average expert combination rule is not only a very simple and intuitive technique of improving the reliability of decision making based on different expert opinions but it is also remarkably robust.
S Ali Hojjatoleslami
