36-737: Applied Multilevel & Hierarchical Models
Fall 2013
Homework Two Solutions
Problem One
A
Corr(yi , yi ) =
Cov (yi ,yi )
V ar (yi )V ar (yi
. We know
V ar(yi )V ar(yi ) = 2 + 2 , so now
only need the covariance. We nd
Cov (yi , yi )
=
Cov ( i ,
=
0
Multilevel & Hierarchical Models
HW04 Solution
December 5, 2013
Problem One
Part A
so we have the likelihood function and prior as
L(x) =
x e
,
x!
f (|, ) 1 e
Applying the slogan, we see that
x e
1 e
x!
f (|x)
= +x1 e( +1)
is again proportional to a Gam