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| kb:hypothesis_testing [2021-05-11 20:04] – jaeyoung | kb:hypothesis_testing [2024-04-30 04:03] (current) – external edit 127.0.0.1 | ||
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| Since we are just comparing P(H0|R=r) and P(H1|R=r), we can cancel out the fR(r) on both sides, so it is equivalent to comparing P(H0)fR|H(r|H0) and P(H1)fR|H(r|H1): | Since we are just comparing P(H0|R=r) and P(H1|R=r), we can cancel out the fR(r) on both sides, so it is equivalent to comparing P(H0)fR|H(r|H0) and P(H1)fR|H(r|H1): | ||
| - | * If $P(H_0) f_{R|H}(r|H_0) > P(H_1) f_{R|H}(r|H_1),thenannounce' | + | * If $P(H_0) f_{R|H}(r|H_0) > P(H_0) f_{R|H}(r|H_0),thenannounce' |
| * If P(H0)fR|H(r|H0)<P(H1)fR|H(r|H1), | * If P(H0)fR|H(r|H0)<P(H1)fR|H(r|H1), | ||
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| The likelihood ratio Λ(r) is defined as: | The likelihood ratio Λ(r) is defined as: | ||
| - | $$ \Lambda(r) = \frac{P(H_1) | + | Λ(r)=fR|H(r|H1)fR|H(r|H0) |
| We can compare this likelihood ratio to the threshold η, which is the ratio between the a priori probabilities: | We can compare this likelihood ratio to the threshold η, which is the ratio between the a priori probabilities: | ||