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