This preview shows page 1. Sign up to view the full content.
Unformatted text preview: pmiss = 0.0, which is unusually good. Of course this small value pmiss is earned at the expense of the
large value of pfalse alarm noted above.
It is important to keep in mind the convention that both pfalse alarm and pmiss are deﬁned as
conditional probabilities.
Any decision rule can be indicated by underlining one element in each column of the likelihood
matrix. For a given rule, pmiss is the sum of entries not underlined in the H1 row of the likelihood
matrix, and pfalse alarm is the sum of the entries not underlined in the H0 row of the likelihood matrix.
This representation allows us to illustrate tradeoﬀs between the two types of error probabilities. If
the underlining in some column is moved from one row to the other, then one error probability increases (because there is one more entry not underlined to include in the sum) and correspondingly,
the other error probability decreases (because there is one fewer entry not underlined to include
in the other sum.) For example, if we were to modify the sample decision rule above by declaring
H0 when X = 1, then pfalse alarm would be reduced from 0.6 to just 0.3 while pmiss would increase
from 0.0 to 0.1. Whether this pair of error probabilities is better t...
View
Full
Document
This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.
 Spring '08
 Zahrn
 The Land

Click to edit the document details