Therefore the map rule is equivalent to the lrt with

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
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.

Ask a homework question - tutors are online