베이즈 정리

R로 배우는 확률 기초

David Robinson

Chief Data Scientist, DataCamp

확률

fair <- rbinom(90000, 20, .5)
sum(fair == 14)
# [1] 3410

dbinom(14, 20, .5) * .9
# [1] 0.03326797

$$\Pr(\text{앞면 14회}|\text{공정})\cdot\Pr(\text{공정})$$

biased <- rbinom(10000, 20, .75)
sum(biased == 14)
# [1] 1706

dbinom(14, 20, .75)  * .1
# [1] 0.01686093

$$\Pr(\text{앞면 14회}|\text{편향됨})\cdot\Pr(\text{편향됨})$$

$$\Pr(\text{편향됨}|\text{앞면 14회})=\frac{\Pr(\text{앞면 14회, 편향됨})}{\Pr(\text{앞면 14회, 편향됨})+\Pr(\text{앞면 14회, 공정})}$$

$$=\frac{\Pr(\text{앞면 14회}|\text{편향됨})\Pr(\text{편향됨})}{\Pr(\text{앞면 14회}|\text{편향됨})\Pr(\text{편향됨}) + \Pr(\text{앞면 14회}|\text{공정})\Pr(\text{공정})}$$

prob_14_fair <- dbinom(14, 20, .5) * .9
prob_14_biased <- dbinom(14, 20, .75) * .1

prob_14_biased / (prob_14_fair + prob_14_biased)

$$\Pr(A|B)=\frac{\Pr(B|A)\Pr(A)}{\Pr(B|A)\Pr(A) + \Pr(B|\text{not }A)\Pr(\text{not }A)}$$

$$A = \text{편향됨}$$

$$B = \text{앞면 14회}$$

R로 배우는 확률 기초