November 2012
Intermediate to advanced
244 pages
7h 15m
English
Content preview from Bayesian Methods in Health Economics
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64 Bayesian Methods in Health Economics
Because of A2. and A3. the relevant conditional distributions are conjugated
and therefore:
p(μ | τ, y)=Normal(μ
n
,σ
2
n
)
= Normal
μ
0
σ
2
0
+
n¯y
σ
2
1
σ
2
0
+
n
σ
2
,
1
1
σ
2
0
+
n
σ
2
(2.17)
and
p(τ | μ, y)=Gamma(α
n
,β
n
)
= Gamma
α
0
+
n
2
,β
0
+
n
i=1
(y
i
− μ)
2
2
(2.18)
(cfr. the analysis of Table 2.3).
Suppose that we observe a sample of n =30data points y:
y
1
=1.2697 y
2
=7.7637 y
3
=2.2532 y
4
=3.4557 y
5
=4.1776
y
6
=6.4320 y
7
= −3.6623 y
8
=7.7567 y
9
=5.9032 y
10
=7.2671
y
11
= −2.3447 y
12
=8.0160 y
13
=3.5013 y
14
=2.8495 y
15
=0.6467
y
16
=3.2371 y
17
=5.8573 y
18
= −3.3749 y
19
=4.1507 y
20
=4.3092
y
21
=11.7327 y
22
=2.6174 y
23
=9.4942 y
24
= −2.7639 y
25
= −1.5859
y
26
=3.6986 y
27
=2.4544
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