
440 Current Trends in Bayesian Methodology with Applications
When we consider the symmetric SV model where ρ ≡ 0, we assume
the inverse gamma prior distribution for σ
2
η
(σ
2
η
∼ IG(n
0
/2, S
0
/2)). Then
the conditional posterior distribution of σ
2
η
is given by the inverse gamma
distribution, σ
2
η
∼ IG(n
1
/2, S
1
/2) where n
1
= n
0
+ n a nd S
1
= S
0
+ (1 −
φ
2
)(h
1
− µ)
2
+
P
n−1
t=1
(h
t+1
− (1 − φ)µ − φh
t
)
2
.
21.2.2 Generation of h: Single-move sam pler
The simplest way to generate h is to g e nerate h
t
given h
−t
= (h
1
, . . . , h
t−1
,
h
t+1
, . . . , h
n
)
′
and θ. Consider the conditional poster ior probability density
function of h
t
,
π(h
t
|h
−t
, θ, y) ∝
exp
−
1
2
h
t
−
1
2
R
2
t
exp(−h
t
) −
1
2σ
2
η
(1 −