STAT 445 Study Guide - Final Guide: Linear Map, Sample Space, Discriminant
10 Apr 2017
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The distribution of x in two populations: population 1: f1(x, population 2: f2(x) Classi cation rule: r1: the set of x for subjects being classi ed as 1, r2: the set of x for subjects being classi ed as 2 where r1 r2 = . (r1 r2 = ) Measures of classi cation accuracy: conditional probabilities: p(2|1) =probabilty of classifying a subject as 2 when it is from 1 f2(x)dx. 1 p(1|2) =probabilty of classifying a subject as 1 when it is from 2 f1(x)dx. =p (x r1| 2) =zr1: marginal probabilities of the accuracy: Given the prior probabilities p1 = p ( 1) and p2 = p ( 2): P (misclassifying a subject as 1) = p2p(1|2) P (misclassifying a subject as 2) = p1p(2|1: total probability of misclassi cation (tpm): T p m = p(1|2)p2 + p(2|1)p1: expected cost of misclassi cation (ecm) R1 = {x : c(2|1)f1(x)p1 c(1|2)f2(x)p2} =(cid:26)x : f1(x) f2(x) c(1|2) c(2|1) p2 p1(cid:27)
