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Unformatted text preview: recall that if is
small, then fi (u) is the approximate probability that the observation is within a length interval
centered at u, if Hi is the true hypothesis. For this reason, we still call fi (u) the likelihood of X = u
if Hi is the true hypothesis. We also deﬁne the likelihood ratio, Λ(u), for u in the support of f1 or
f0 , by
A likelihood ratio test (LRT) with threshold τ is deﬁned by:
Λ(X ) >τ
<τ declare H1 is true
declare H0 is true. Just as for the case of discrete-type observations, the maximum likelihood (ML) test is the LRT
with threshold τ = 1, and the maximum a posteriori probability (MAP) decision rule is the LRT 114 CHAPTER 3. CONTINUOUS-TYPE RANDOM VARIABLES with threshold τ = π0 , where (π1 , π0 ) is the prior probability distribution. In particular, the ML
rule is the special case of the MAP rule for the uniform prior: π1 = π0 . The following deﬁnitions
are the same as in the case of discrete-type observations:
pfalse alarm = P (de...
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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 Institute of Technology.
- Spring '08
- The Land