<s>
Umbrella	B-Algorithm
sampling	I-Algorithm
is	O
a	O
technique	O
in	O
computational	B-Algorithm
physics	I-Algorithm
and	O
chemistry	O
,	O
used	O
to	O
improve	O
sampling	O
of	O
a	O
system	O
(	O
or	O
different	O
systems	O
)	O
where	O
ergodicity	O
is	O
hindered	O
by	O
the	O
form	O
of	O
the	O
system	O
's	O
energy	O
landscape	O
.	O
</s>
<s>
It	O
is	O
a	O
particular	O
physical	O
application	O
of	O
the	O
more	O
general	O
importance	B-Algorithm
sampling	I-Algorithm
in	O
statistics	O
.	O
</s>
<s>
In	O
Metropolis	B-Algorithm
Monte	I-Algorithm
Carlo	I-Algorithm
runs	O
,	O
the	O
low	O
probability	O
of	O
overcoming	O
the	O
potential	O
barrier	O
can	O
leave	O
inaccessible	O
configurations	O
poorly	O
sampled	O
—	O
or	O
even	O
entirely	O
unsampled	O
—	O
by	O
the	O
simulation	O
.	O
</s>
<s>
Umbrella	B-Algorithm
sampling	I-Algorithm
is	O
a	O
means	O
of	O
"	O
bridging	O
the	O
gap	O
"	O
in	O
this	O
situation	O
.	O
</s>
<s>
Series	O
of	O
umbrella	B-Algorithm
sampling	I-Algorithm
simulations	O
can	O
be	O
analyzed	O
using	O
the	O
weighted	O
histogram	O
analysis	O
method	O
(	O
WHAM	O
)	O
or	O
its	O
generalization	O
.	O
</s>
<s>
Subtleties	O
exist	O
in	O
deciding	O
the	O
most	O
computationally	O
efficient	O
way	O
to	O
apply	O
the	O
umbrella	B-Algorithm
sampling	I-Algorithm
method	O
,	O
as	O
described	O
in	O
Frenkel	O
&	O
Smit	O
's	O
book	O
Understanding	O
Molecular	O
Simulation	O
.	O
</s>
<s>
Alternatives	O
to	O
umbrella	B-Algorithm
sampling	I-Algorithm
for	O
computing	O
potentials	O
of	O
mean	O
force	O
or	O
reaction	O
rates	O
are	O
free	O
energy	O
perturbation	O
and	O
transition	O
interface	O
sampling	O
.	O
</s>
