<s>
In	O
mathematics	O
,	O
more	O
specifically	O
in	O
the	O
theory	O
of	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
,	O
variance	B-Algorithm
reduction	I-Algorithm
is	O
a	O
procedure	O
used	O
to	O
increase	O
the	O
precision	B-General_Concept
of	O
the	O
estimates	O
obtained	O
for	O
a	O
given	O
simulation	O
or	O
computational	O
effort	O
.	O
</s>
<s>
Every	O
output	O
random	O
variable	O
from	O
the	O
simulation	O
is	O
associated	O
with	O
a	O
variance	O
which	O
limits	O
the	O
precision	B-General_Concept
of	O
the	O
simulation	O
results	O
.	O
</s>
<s>
In	O
order	O
to	O
make	O
a	O
simulation	O
statistically	O
efficient	O
,	O
i.e.	O
,	O
to	O
obtain	O
a	O
greater	O
precision	B-General_Concept
and	O
smaller	O
confidence	O
intervals	O
for	O
the	O
output	O
random	O
variable	O
of	O
interest	O
,	O
variance	B-Algorithm
reduction	I-Algorithm
techniques	O
can	O
be	O
used	O
.	O
</s>
<s>
The	O
main	O
ones	O
are	O
common	O
random	O
numbers	O
,	O
antithetic	B-Algorithm
variates	I-Algorithm
,	O
control	B-Algorithm
variates	I-Algorithm
,	O
importance	B-Algorithm
sampling	I-Algorithm
,	O
stratified	O
sampling	O
,	O
moment	O
matching	O
,	O
conditional	O
Monte	O
Carlo	O
and	O
quasi	O
random	O
variables	O
.	O
</s>
<s>
For	O
simulation	O
with	O
black-box	O
models	O
subset	B-Algorithm
simulation	I-Algorithm
and	O
line	B-Algorithm
sampling	I-Algorithm
can	O
also	O
be	O
used	O
.	O
</s>
<s>
Under	O
these	O
headings	O
are	O
a	O
variety	O
of	O
specialized	O
techniques	O
;	O
for	O
example	O
,	O
particle	O
transport	O
simulations	O
make	O
extensive	O
use	O
of	O
"	O
weight	O
windows	O
"	O
and	O
"	O
splitting/Russian	O
roulette	O
"	O
techniques	O
,	O
which	O
are	O
a	O
form	O
of	O
importance	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
Because	O
the	O
standard	O
deviation	O
only	O
converges	O
towards	O
at	O
the	O
rate	O
,	O
implying	O
one	O
needs	O
to	O
increase	O
the	O
number	O
of	O
simulations	O
(	O
)	O
by	O
a	O
factor	O
of	O
to	O
halve	O
the	O
standard	O
deviation	O
of	O
,	O
variance	B-Algorithm
reduction	I-Algorithm
methods	O
are	O
often	O
useful	O
for	O
obtaining	O
more	O
precise	O
estimates	O
for	O
without	O
needing	O
very	O
large	O
numbers	O
of	O
simulations	O
.	O
</s>
<s>
The	O
common	O
random	O
numbers	O
variance	B-Algorithm
reduction	I-Algorithm
technique	O
is	O
a	O
popular	O
and	O
useful	O
variance	B-Algorithm
reduction	I-Algorithm
technique	O
which	O
applies	O
when	O
we	O
are	O
comparing	O
two	O
or	O
more	O
alternative	O
configurations	O
(	O
of	O
a	O
system	O
)	O
instead	O
of	O
investigating	O
a	O
single	O
configuration	O
.	O
</s>
