18HTPerfandEx - Hypothesis Testing Performance and Examples...

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EE 3180 Probability and Random  Signal Analysis, ©2009 by J. B. Burl 1 Hypothesis Testing:  Performance and Examples Jeffrey B. Burl
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EE 3180 Probability and Random  Signal Analysis, ©2009 by J. B. Burl 2 Outline Define terms in the average cost. Discuss performance analysis. Examples. Define sufficient statistics.
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EE 3180 Probability and Random  Signal Analysis, ©2009 by J. B. Burl 3 The Average Cost The average cost is defined: 00 0 0 0 00 0 ( ) ( | ) ( ) (Null Detection) C C P H P D H C P H P = 01 1 0 1 01 1 ( ) ( | ) ( ) (Missed Detection) C P H P D H C P H P + 10 0 1 0 10 0 ( ) ( | ) ( ) (False Alarm) C P H P D H C P H P + 11 1 1 1 11 1 ( ) ( | ) ( ) (Detection) C P H p D H C P H P +
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EE 3180 Probability and Random  Signal Analysis, ©2009 by J. B. Burl 4 Performance Analysis We can compute the probabilities in the  average cost to understand performance: 0 0 0 0 | 0 ( | ) (Null Detection) ( | ) ND r H Z P D H P P f R H dR = = = 1 0 0 1 | 1 ( | ) (Missed Detection) ( | ) M r H Z P D H P P f R H dR = = = 0 1 1 0 | 0 ( | ) (False Alarm) ( | ) F r H Z P D H P P f R H dR = = = 1 1 1 1 | 1 ( | ) (Detection) ( | ) D r H Z P D H P P f R H dR = = =
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EE 3180 Probability and Random  Signal Analysis, ©2009 by J. B. Burl 5 Performance Analysis, Cont. Defining the regions Z 0  and Z 1  may be  difficult, and performing the integral over  these regions may be more difficult. Instead, we can evaluate these probabilities,  as shown on the next page, if we can find a  density functions for the random variables: Λ (R|H 0 ) or ln  Λ (R |H 0 ) Λ (R|H 1 ) or ln  Λ (R |H 1 )
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This note was uploaded on 06/16/2010 for the course EE ee3180 taught by Professor Burl during the Spring '10 term at Michigan Technological University.

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18HTPerfandEx - Hypothesis Testing Performance and Examples...

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