MIT6_262S11_lec21

# 1 q0a q1a q0 q1 1 0 i q

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Unformatted text preview: } = p0q0(η ) + p1q1(η ) = p0[q0(η ) + η q1(η )] q0(η ) + η q1(η ) ≤ q0(A) + η q1(A); by MAP 8 q0(η ) + η q1(η ) ≤ q0(A) + η q1(A); by MAP Note that the p oint q0(A), q1(A) does not depend on p0; the a priori probabilities were simply used to prove the above inequality. 1 q0(A) + η q1(A) ❜ ❜ q0(η ) + η q1(η ) ❜ ❜ ❜ ❜ ❜ ❜ ❜￿ 1 0 ❜ ❜ ❜ ❜ ❜ i ❜ ❜ ❜ ❜ ❜ ❜￿ ❜ ❜ ❜ ❜ ❜ ❜ (q (A), q (A)) q (A) = Pr {e | H =i} for test A q0(η ) slope −η q1(η ) 1 For every A and every η , (q0(A), q1(A)) lies NorthEast of the line of slope −η through (q0(η ), q1(η )). Thus (q0(A), q1(A)) is NE of the upper envelope of these straight lines. 9 1 u(α) q0(η ) + η q1(η ) ✈ 1 0 ❜ ❜ ❜ ❜ ❜ ◗ ❦ ❜ ◗ ❜ ◗ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❜ ❜ (q (A), q (A)) increasing η q0(η ) slope −η α q1(η ) 1 If the vertical axis of the error curve is inverted, it is called a receiver operating curve (ROC) which is a staple of radar system design. The Neyman-Pearson test is a test that chooses A...
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## This note was uploaded on 01/13/2012 for the course ELECTRICAL 6.262 taught by Professor Staff during the Fall '11 term at MIT.

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