Information Technology Reference
In-Depth Information
-
How many observations should one collect to ensure a specified statistical
accuracy ?
-
Given
N
observations from a Monte Carlo Experiment, how accurate is the
estimated solution ?
Both question are answered and discussed in [15]. Using the Chebyshev's inequal-
ity and specifying a
confidence level
1
δ
, one can determine the smallest sample
size
N
that guarantees an integration error no larger than
.In[15]thisspec-
ification is called the (
, δ
)
absolute error criterion
and leads to the worst-case
sample size
−
1
/
4
δ
2
N
:=
(6)
5.2
Monte Carlo Hyperspheres Volume Integration
Using equations (5) and (6) a simple algorithm can be developed which esti-
mates the total space (volume) covered by the hyperspheres inside the unitary
hypercube [0
,
1]
n
.
Algorithm 1.
Monte Carlo Hyperspheres Volume Integration
input
:
H
= set of hyperspheres,
= absolute error of the estimated volume,
δ
= confidence level
output
: total volume of
H
begin
1
inside
←−
0
2
// calculate required worst-case
// sample size
N
N ←−
1
/
4
δ
2
3
for
i ←
1
to
N
do
4
random point from [0
,
1]
n
x
←−
5
foreach
h ∈ H
do
6
if
dist
(
c
h
,
x
)
≤ r
h
then
7
//
c
h
is center of
h, r
h
is radius of
h
inside
←−
inside + 1
8
goto 5:
9
return
(inside
/N
)
10
end
11
6
Limitation of Real-Valued Negative Selection in Higher
Dimensions
In [6] an immune inspired real-valued negative selection algorithm was compared
to different statistical anomaly detection techniques
5
for a high-dimensional
5
Parzen-Window, one class SVM.
