Geoscience Reference
In-Depth Information
p
R
i
a
i
1
a
i
P
f
l
i
M
i
g Ub
M
i
R
i
a
i
ð
Þ=
ð
Þ
c
ð
3
:
35
Þ
M
i
during the whole procedure of an exhaustive
search for values of the ith component according to the Boolean formula is esti-
mated by the inequality:
The probability of realizing
ʼ
i
≤
h
n
o
i
¼ 1
D
i
p
R
i
a
i
1
a
i
X
ð
1
;
2
; ...;
N
i
Þ
1
N
i
1
U
ð
M
i
R
i
a
i
Þ=
ð
Þ
Given that a certain small value is expressed by
D
t
, we obtain an extra condition
—
except from (
3.34
) to determine mi:
i
:
p
q
i
a
i
1
a
i
Ub
M
i
q
i
a
i
ð
Þ=
ð
Þ
c
¼1
D
i
=
N
i
;
ð
3
:
36
Þ
α
i
-
where q
i
=m
i
/
d
i
/n
i
.
Thus, if the delay capacities are calculated from Eq. (
3.36
), the probability of
error for the whole system will equal to:
P
m
¼ 1
Y
K
i¼1
X
ð
1
;
2
; ...;
N
i
Þ
because of the over
ow of the memory.
The evaluation of probability of the on-board computer memory over
fl
owing
under monitoring conditions of processing information through the K channels as
considered above enables one
fl
—
in de
nite situations
—
to calculate the parameters
of the system, to estimate its ef
cacy, and to choose one of the two processing
methods which has already been indicated above. Both delay variants discussed
above are equivalent in the requisite additional memory capacity and operation
time. Indeed, if
first variant equals the
number of variants considered in the second. Similarly, assuming qi
i
=
ʔ
i
=
˃
i
, then r
i
=R
i
, i.e. the delay in the
ʵ
i
, we obtain
the equality ri
i
=R
i
. Therefore, the choice of the kind of delay should be determined
by technical considerations of its realization.
3.6 Applications of the Sequential Decision-Making
Procedure
Sequential analysis applications are mainly occurred when the under study sto-
chastic processes are time-dependent and the researcher is not able to form repre-
sentative samples. Carvalho and Lopes (2007) developed and implemented a
simulation-based sequential algorithm to estimate a univariate Markov switching
stochastic volatility model and showed that the sequential algorithm can perform
accurate sequential inferences. It was shown that a useful tool for modeling time
varying variables and for measure of risk is stochastic volatility models.
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