STAT1302 Probability and Statistics II
Jianfeng Yao
Suciency Principle
T:
Sucient statistic
Sample A - Data XA
tA = T (XA )
Sample B - Data XB
tB = T (XB )
inference B
If
tA = tB
then
inference A inference B.
inference A
Example: marriage/divorce pb.
Ba
STAT1302 Probability and Statistics II
Jianfeng Yao
Example: Poisson data
X, Y
independent, Poisson P()
y
.
.
.
p( x, y |)
3
2
.
1
-2x+y
.
.
0
e
= -x! y!
x
1
2
3
Having known X , does it help to know Y too ?
[ Conditional distribution of Y given X . ]
y
.