Bayes theorem

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3

4

? 5

Total probability theory, Bayes rule

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? 1.0 8

Excercise 9

Why does Bayes’ rule have important meaning ?

probability vs. statistics sampling inference statistics probability vs. statistics

90% 98% 1% 12

1% 90% 10% 99% 2% 98% 13

1% 90% 10% 99% 2% 98% 14

10% of 1% 90% of 1% 1% 1% 90% 10% 99% 2% of 99% 99% 2% 98% 98% of 99% 15

10% of 1% 90% of 1% 1% 99% 2% of 99% 98% of 99% 16

X\Y 1 2 1/2 1/4 T 1.0 X\Y 1 2 T 1/8 1/4 1/2 1.0 X\Y 1 2 T 1/2 1.0 1/4

1% 99% 90% 98% 10% 2% 0.9% 97.02% 0.1% 1.98% 99.9% 0.1% 31.2% 68.8% 2.88% 97.12% 18

A=au+cw B=bu+dw y1 y2 x1 a b u x2 c d w y1 y2 x1 au bu x2 cw dw A B y1 au/A bu/B x2 cw/A dw/B A=au+cw B=bu+dw 19

98% 90% 1% 20

/ 21

Thomas Bayes (1702-1761) 22

1% 99% 90% 98% 10% 2% 99.9% 0.1% 31.2% 68.8% / Prior, Posterior 23

Thank you !!