
6 Current Trends in Bayesian Methodology with Applications
resampling schemes in which low variance resampling is used only in those it-
erations in which the weights have high variance; see [17] for a summary of
such improvements.
Algorithm 1.1 The SIR Algorithm targetting {˜π
n
}
n≥1
Iteration n = 1:
Sample X
1
1,1
, . . . , X
N
1,1
iid
∼ µ
Calculate weights, for i = 1, . . . , N : w(X
i
1,1
) ∝ ˜π
1
(X
i
1,1
)/µ(X
i
1,1
).
Normalise weights, for i = 1, . . . , N: W
i
1
= w(X
1
1,1
)/
P
N
j=1
w(X
j
1,1
).
Iteration n ≥ 2:
Resample {X
i
n−1,1:n−1
, W
i
n−1
}
N
i=1
to obtain {
¯
X
i
n−1,1:n−1
, 1/N}
n
i=1
.
for i = 1, . . . , N: sample X
i
n,n
∼ q
n
(·|
¯
X
i
n−1,1:n−1
).
for i = 1, . . . , N: set X
i
n,1:n
= (
¯
X
i