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Unformatted text preview: iding H0 is true if
Λ(X ) < 1. The ML rule can be compactly written as
Λ(X ) > 1 declare H1 is true
< 1 declare H0 is true. We shall see that the other decision rule,
as an LRT, but with the threshold 1 changed
<τ described in the next section, can also be expressed
to diﬀerent values. An LRT with threshold τ can be
declare H1 is true
declare H0 is true. Note that if the threshold τ is increased, then there are fewer observations that lead to deciding H1
is true. Thus, as τ increases, pfalse alarm decreases and pmiss increases. For most binary hypothesis
testing problems there is no rule that simultaneously makes both pfalse alarm and pmiss small. In a
sense, the LRT’s are the best possible family of rules, and the parameter τ can be used to select a
given operating point on the tradeoﬀ between the two error probabilities. As noted above, the ML
rule is an LRT with threshold τ = 1. 2.11.2 Maximum a posteriori probability (MAP) decision rule The other decision rule we discuss req...
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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.
- Spring '08
- The Land