chapter4

1.0 1.5 ! 2.0 1.5 2.0 1.0 1.5 ! 2.0 1.0 1.5 2.0 1.0 1.5 ! 2.0 1.0 0.0 1.0 0.0 1.0 0.0 2.0 1.0 1.0 2.0...

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1.0

1.5 !

2.0

1.5

2.0

1.0

1.5 !

2.0

1.0

1.5

2.0

1.0

1.5 !

2.0

1.0 0.0

1.0 0.0

1.0 0.0

2.0 1.0

1.0

2.0

2.0

2.0

1.5

2.0

1.0

S=1000

0.0

1.0

2.0

S=100

0.0

0.0

1.0

2.0

S =10

0 200 600 1000 # of Monte Carlo samples 0 200 600 1000 # of Monte Carlo samples 0 200 600 1000 # of Monte Carlo samples

cumulative mean 1.45 1.50

cumulative 97.5% quantile 1.4 1.5 1.6 1.7 1.8 1.9

cumulative cdf at 1.75 0.90 0.94 0.98

1.40

!4 !2 0 ! 2 4 !4 !2 0 ! 2 4

0

0.00

1

0.05

p( !|y1...yn) 2 3 4

p (!) 0.10 0.15

5

0.20

1.0 1.5 ! = "1 "2 2.0

0.0

0.5

p( !|y1,y2) 1.0 1.5 2.0

!10 !5 0 ~ ~ D = Y1 ! Y2 5 10

0

500

p(D|y1,y2) 1000 1500 2000

1.5 0.0

0.00

0.5

Pr(Y i = y i ) 0.10 0.20

1.0

0.30

empirical distribution predictive distribution

0

2

4 6 number of children

8

0.5

1.0

1.5 ~ t(Y)

2.0

2.5