| 116 |
The decision rule we use is in fact well known as Bayes Decision Rule
...[P w 1 x >P w 2 x >x is relevant,x is non relevant]D 1 The expression D 1 is a short hand notation for the following:compare P w 1 x with P w 2 x if the first is greater than the second then decide that x is relevant otherwise decide x is non relevant
...The meaning of [E >p,q]is that if E is true then decide p,otherwise decide q
...In other words once we have decided one way e
...This sum will be minimised by making P error x as small as possible for each x since P error x and P x are always positive
...Of course average error is not the only sensible quantity worth minimising
...R wi x li 1 P w 1 x li 2 P w 2 x i 1,2 The overall risk is a sum in the same way that the average probability of error was,R wi x now playing the role of P wi x
...[R w 1 x <R w 2 x >x is relevant,x is non relevant]D 2 |
