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Bayes theorem.

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Presentation on theme: "Bayes theorem."— Presentation transcript:

1 Bayes theorem

2 ? 2

3 3

4 4

5 ? 5

6 Total probability theory, Bayes rule

7 ? 7

8 ? 1.0 8

9 Excercise 9

10 Why does Bayes’ rule have important meaning ?

11 probability vs. statistics
sampling inference statistics probability vs. statistics

12 90% 98% 1% 12

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

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

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

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

17 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

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

19 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

20 98% 90% 1% 20

21 / 21

22 Thomas Bayes ( ) 22

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

24 Thank you !!


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