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 !!