here is a
hypothesis that may be true (state
or false (state
is the assertion of the hypothesis. The penalty function
has the property
Such property enforces greater penalty for the false decision then for the
correct one for every prior state.
Given the observation
we choose the decision
stands for ''threshold''. This result is called ''likelihood ratio test''.
Note, that if
then the rule simply says ''choose
With the decision rule
known one may compute an apriori probability of the correct judgement