
74 Current Trends in Bayesian Methodology with Applications
FIGURE 3.3
Joint pos terior reference density π(θ
1
, θ
2
|r
1
, r
2
, n
1
, n
2
), when r
1
= 5 1,
n
1
= 8 197, r
2
= 7 4 and n
2
= 8 198.
a p-value of 0.04. Morever, the re sults suggested an estimated vaccine effi-
cacy (one minus the relative hazard rate of HIV in the vaccine versus placebo
group) of
VE(r
1
, n
1
, r
2
, n
2
) = 1 −
r
1
/n
1
r
2
/n
2
= 0 .31.
An objective Bayesian, intrinsic reference analysis of these data will now be
provided.
The joint refere nce posterior distribution for θ
1
and θ
2
which corre-
sp onds to the overall reference prior π(θ
1
, θ
2
) = Be(θ
1
|
1
2
,
1
2
) Be(θ
2
|
1
2
,
1
2
) is
π(θ
1
, θ
2
|r
1
, r
2
, n
1
, n
2
) = Be(θ
1
|51