For most binary hypothesis testing problems there is

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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 trade-offs 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...
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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.

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