e have seen in the previous section that the
precision
is more natural then
for Bayesian computations involving normal distribution. We are given a sample
from
,
where the parameters
and
are unknown. Assume the following prior for the mean
and precision
:
|
|
(Normal distribution with unknown parameters 1)
|
where the gamma distribution has the following
form:
|
|
(Gamma distribution)
|
and the constants
are known. As usual in Bayesian computation, we disregard multiplicative
constants. The expression for the prior distribution takes the
form
We multiply it with the
likelihood
and obtain the joint posterior distribution of
:
|
|
(Normal distribution with unknown parameters 2)
|
|
