Isye 2027

# Therefore the map rule is equivalent to the lrt with

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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 written as >τ Λ(X ) <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.

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