Statistical Detection Theory Statistical Detection Theory I Wenhui Xiong NCL UESTC whxiong@uestc.edu.cn
whxiong@uestc.edu.cn Statistical Detection Theory Statistical Detection Theory I Wenhui Xiong NCL UESTC
Outline Deterministic Approach Neyman-Person Theorem Receiver Operation Characteristics ●Bayesian Approach Minimum Probability of Error 。Bayes Risk Multiple Hypothesis Test whxiong@uestc.edu.cn 2
whxiong@uestc.edu.cn Deterministic Approach Neyman-Person Theorem Receiver Operation Characteristics Bayesian Approach Minimum Probability of Error Bayes Risk Multiple Hypothesis Test Outline 2
Neyman-Person Theorem (1/7) Detection is Hypothesis test from observations whxiong@uestc.edu.cn 3
whxiong@uestc.edu.cn Neyman-Person Theorem (1/7) 3 Detection is Hypothesis test from observations
Neyman-Person Theorem (1/7) Detection is Hypothesis test from observations Ho Nothing but noise Null hypo. whxiong@uestc.edu.cn 4
whxiong@uestc.edu.cn Neyman-Person Theorem (1/7) 4 Detection is Hypothesis test from observations H0 Nothing but noise Null hypo
Neyman-Person Theorem (1/7) Detection is Hypothesis test from observations Ho Nothing but noise Null hypo. H Something with noise Alternative hypo. whxiong@uestc.edu.cn 5
whxiong@uestc.edu.cn Neyman-Person Theorem (1/7) 5 Detection is Hypothesis test from observations H0 Nothing but noise Null hypo. H1 Something with noise Alternative hypo
Neyman-Person Theorem (1/7) Detection is Hypothesis test from observations Ho Nothing but noise Null hypo. Something with noise Alternative hypo. Goal:Infer from x[n],what is true.Ho or H whxiong@uestc.edu.cn 6
whxiong@uestc.edu.cn Neyman-Person Theorem (1/7) 6 Detection is Hypothesis test from observations H0 Nothing but noise Null hypo. H1 Something with noise Alternative hypo. Goal: Infer from x[n], what is true. H0 or H1
Neyman-Person Theorem (1/7) Detection is Hypothesis test from observations Ho Nothing but noise Null hypo. H Something with noise Alternative hypo. Goal:Infer from x[n],what is true.Ho or Hi Example Detect DC in WGN Ho cin]=wlnl Hy xIn]=A+wln] whxiong@uestc.edu.cn 7
whxiong@uestc.edu.cn Neyman-Person Theorem (1/7) 7 Detection is Hypothesis test from observations Example : Detect DC in WGN H0 x[n] = w[n] H1 x[n] = A + w[n] H0 Nothing but noise Null hypo. H1 Something with noise Alternative hypo. Goal: Infer from x[n], what is true. H0 or H1
NP theorem (2/7) Binary Hypo.Test:Ho or H1:one of them Happens for sure whxiong@uestc.edu.cn 8
whxiong@uestc.edu.cn NP theorem (2/7) Binary Hypo. Test: H0 or H1:one of them Happens for sure 8
NP theorem (2/7) Binary Hypo.Test:Ho or H1:one of them Happens for sure p(H;H):Prob.(decide H when Ho is true)False alarm p(Ho:H):Prob.(decide Ho when H is true)Miss Detection p(Ho:Ho):Prob.(decide Ho when Ho is true)Non-Detection p(HH):Prob.(decide H when H is true)Detection! whxiong@uestc.edu.cn 9
whxiong@uestc.edu.cn NP theorem (2/7) Binary Hypo. Test: H0 or H1:one of them Happens for sure 9 •p(H1 ;H0 ): Prob.(decide H1 when H0 is true) False alarm •p(H0 ;H1 ): Prob.(decide H9 when H1 is true) Miss Detection • p(H0 ;H0 ): Prob.(decide H0 when H0 is true) Non-Detection • p(H1 ;H1 ): Prob.(decide H1 when H1 is true) Detection!
NP theorem (2/7) Binary Hypo.Test:Ho or H1:one of them Happens for sure p(H;H):Prob.(decide H when Ho is true)False alarm p(Ho:H):Prob.(decide Ho when H is true)Miss Detection p(Ho:H):Prob.(decide Ho when Ho is true)Non-Detection p(H;H):Prob.(decide H when H is true)Detection! .Type I error:decide H when Ho is true:PrA Type II error:decide Ho when H is true:1-Pp Our Goal is to minimize error! whxiong@uestc.edu.cn 10
whxiong@uestc.edu.cn NP theorem (2/7) Binary Hypo. Test: H0 or H1:one of them Happens for sure 10 •p(H1 ;H0 ): Prob.(decide H1 when H0 is true) False alarm •p(H0 ;H1 ): Prob.(decide H9 when H1 is true) Miss Detection • p(H0 ;H0 ): Prob.(decide H0 when H0 is true) Non-Detection • p(H1 ;H1 ): Prob.(decide H1 when H1 is true) Detection! Our Goal is to minimize error! • Type I error: decide H1 when H0 is true: PFA •Type II error: decide H0 when H1 is true: 1-PD