<s>
The	O
VEGAS	B-Algorithm
algorithm	I-Algorithm
,	O
due	O
to	O
G	O
.	O
Peter	O
Lepage	O
,	O
is	O
a	O
method	O
for	O
reducing	B-Algorithm
error	I-Algorithm
in	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulations	I-Algorithm
by	O
using	O
a	O
known	O
or	O
approximate	O
probability	O
distribution	O
function	O
to	O
concentrate	O
the	O
search	O
in	O
those	O
areas	O
of	O
the	O
integrand	O
that	O
make	O
the	O
greatest	O
contribution	O
to	O
the	O
final	O
integral	O
.	O
</s>
<s>
The	O
VEGAS	B-Algorithm
algorithm	I-Algorithm
is	O
based	O
on	O
importance	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
The	O
GNU	B-Application
Scientific	I-Application
Library	I-Application
(	O
GSL	O
)	O
provides	O
a	O
VEGAS	O
routine	O
.	O
</s>
<s>
In	O
practice	O
it	O
is	O
not	O
possible	O
to	O
sample	O
from	O
the	O
exact	O
distribution	O
g	O
for	O
an	O
arbitrary	O
function	O
,	O
so	O
importance	B-Algorithm
sampling	I-Algorithm
algorithms	O
aim	O
to	O
produce	O
efficient	O
approximations	O
to	O
the	O
desired	O
distribution	O
.	O
</s>
<s>
The	O
VEGAS	B-Algorithm
algorithm	I-Algorithm
approximates	O
the	O
exact	O
distribution	O
by	O
making	O
a	O
number	O
of	O
passes	O
over	O
the	O
integration	O
region	O
while	O
histogramming	O
the	O
function	O
f	O
.	O
Each	O
histogram	B-Algorithm
is	O
used	O
to	O
define	O
a	O
sampling	O
distribution	O
for	O
the	O
next	O
pass	O
.	O
</s>
<s>
In	O
order	O
to	O
avoid	O
the	O
number	O
of	O
histogram	B-Algorithm
bins	O
growing	O
like	O
with	O
dimension	O
d	O
the	O
probability	O
distribution	O
is	O
approximated	O
by	O
a	O
separable	O
function	O
:	O
so	O
that	O
the	O
number	O
of	O
bins	O
required	O
is	O
only	O
Kd	O
.	O
</s>
