Weight matrix Models Iii S=S, S3 345063708 S9 P(S|+)P3(S)P2(S2)P1(S3)P5(S)P6(S) Odds ratio: R P(S)-)Pbg(S1)Pbg(S2)Pbg(S3)o Pbg(S8)Pbg(Sg) ∏P4+(SP(S) Score s=log2R =>log2(P 4+(Sk)/Pba(S) Neyman-Pearson Lemma Optimal decision rules are of the form>C EquiV. log2 (R)>c because log is a monotone functionWeight Matrix Models III S = S1 S2 S3 S4 S5 S6 S7 S8 S9 P(S|+) P-3 ( S1)P-2 ( S 2)P-1 ( S 3) ••• P 5 ( S 8)P 6 ( S 9 ) Odds Ratio: R = = P(S|-) Pbg ( S1)Pbg ( S 2)Pbg ( S 3) ••• Pbg ( S 8)Pbg ( S 9) k=9 = ∏ P-4+ k ( S k)/ Pbg ( S k) k=1 k=9 Score s = log 2R = ∑ log2 (P-4+ k ( S k)/ Pbg ( S k)) k=1 Neyman-Pearson Lemma: Optimal decision rules are of the form R > C Equiv.: log 2(R) > C ’ because log is a monotone function