Bayesian Revision

K

L

M

N

O

Total 1

Total 0.0748

Probability

A B C D E F G H I J 1 Bayesian Revision Market Share 2 Binomial 3 p 0.1 0.2 0.3 0.4 0.5 0.6 4 Prior 0.05 0.15 0.2 0.3 0.2 0.1 5 6 New Evidence 7 n 20 x 4 8 9 10 Joint Prob. 0.0045 0.0327 0.0261 0.0105 0.0009 0.0000 11 12 Posterior 0.0601 0.4379 0.3489 0.1404 0.0124 0.0004 13 14 15 Bayesian Revision - Binomial 16 0.45 17 0.4 18 0.35 19 0.3 20 21 0.25 22 0.2 23 0.15 24 0.1 25 26 0.05 27 0 28 0.1 0.2 0.3 0.4 0.5 0.6 Colu Colu 29 mn I mn J 30 p 31 32

Row 5 Row 13

Colu mn K

Colu mn L

Probability

A B C D E F G H I J K L 1 Bayesian Revision 2 Poisson 3 λ 1 2 3 4 4 Prior 0.1 0.5 0.2 0.2 5 6 New evidence 7 Observed 2 8 9 Joint Prob. 0.0184 0.1353 0.0448 0.0293 10 11 Posterior 0.0807 0.5940 0.1967 0.1286 12 13 14 Bayesian Revision - Poisson 15 0.6 16 0.55 17 0.5 18 0.45 19 0.4 20 0.35 21 0.3 22 0.25 23 0.2 24 0.15 25 0.1 26 0.05 27 0 28 1 2 3 4 Colum Colum Colum Colum Colum Colum nG nH nI nJ nK nL 29 30  31

M

N

Total 1

0.2278

Row 5 Row 12

O

J

K

L

M

4.07

f(x)

A B C D E F G H I 1 Bayesian Revision Average stock return 2 Normal 3 Prior 4 5 M 15 σ(M) 8 6 New Evidence 7 n 10 x-bar 11.54 s 6.8 8 9 Posterior Credible sets 10 11 1−α M 11.77 σ(M) 2.08 95% 11.77 + or 12 13 Bayesian Revision - Normal 14 15 1 16 0.9 17 0.8 18 19 0.7 20 0.6 21 22 0.5 23 0.4 24 0.3 25 26 0.2 27 0.1 28 0 29 0 0.1 0.2 0.3 0.4 0.5 0.6 30 31 x 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

0.7

0.8

0.9

1

N

O

Bayesian Revision based on Empirical Conditional Probabilities Growth s1 Prior Probability 0.2

Decline s2 0.3

Conditional Probabilities s1 s2 Good P(I1 | .) 0.8 0.1 Bad P(I2 | .) 0.2 0.7 Neutral P(I3 | .) 0 0.2 P(I4 | .) P(I5 | .) Total 1 1 Joint Probabilities s1 I1 0.1600 I2 0.0400 I3 0.0000 I4 I5

s2 0.0300 0.2100 0.0600

Posterior Probabilities s1 s2 P(. | I1) 0.7442 0.1395 P(. | I2) 0.1000 0.5250 P(. | I3) 0.0000 0.1558 P(. | I4) P(. | I5)

Same s3 0.5

s4

s5

s6

s7

s3 0.05 0.3 0.65

s4

s5

s6

s7

1

0

0

0

0

s3 0.0250 0.1500 0.3250

s4

s5

s6

s7

s3 0.1163 0.3750 0.8442

s4

s5

s6

s7

s8

Total 1

s8

0

s8

s8

Marginal 0.2150 0.4000 0.3850