
326 Current Trends in Bayesian Methodology with Applications
1. Compute the random expected utility
Ψ
C
(r
′
, r, x) =
Z
"
X
M
1
,M
2
,M
3
p
M
1
M
2
M
3
x
U
C
(c)
#
P
A
(c|r
′
, x) dc.
2. Compute the random expected utility
Ψ
C
(r, x) =
Z
Ψ
C
(r
′
, r, x)P
A
(r
′
|r, x) dr
′
.
3. Compute the random optimal alternative R(x) = arg max
r
Ψ
C
(r, x).
Then, we would have an estimate of the desired distribution h(r|x) in (15.6),
through p
A
(R ≤ r|x) = Pr(R(x) ≤ r). In order to estimate R(x), we may
proceed by simulation as outlined in Algorithm 15.2.
Algorithm 15.2 Simulating the optimal planned evasion level
For each x
For i = 1 to K
Sample U
i
C
(·), P
i
A
(c|·), P
i
A
(r
′
|·).
Compute
Ψ
i
C
(r
′
, r, x) =
Z
X
M
1
,M
2
,M
3
p
M
1