MIT6_262S11_lec21

1 q0a q1a q0 q1 1 0 i q

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: } = 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...
View Full Document

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.

Ask a homework question - tutors are online