<s>
The	O
root-mean-square	B-General_Concept
deviation	I-General_Concept
(	O
RMSD	B-General_Concept
)	O
or	O
root-mean-square	B-General_Concept
error	I-General_Concept
(	O
RMSE	B-General_Concept
)	O
is	O
a	O
frequently	O
used	O
measure	O
of	O
the	O
differences	O
between	O
values	O
(	O
sample	O
or	O
population	O
values	O
)	O
predicted	O
by	O
a	O
model	O
or	O
an	O
estimator	O
and	O
the	O
values	O
observed	O
.	O
</s>
<s>
The	O
RMSD	B-General_Concept
represents	O
the	O
square	O
root	O
of	O
the	O
second	O
sample	O
moment	O
of	O
the	O
differences	O
between	O
predicted	O
values	O
and	O
observed	O
values	O
or	O
the	O
quadratic	B-General_Concept
mean	I-General_Concept
of	O
these	O
differences	O
.	O
</s>
<s>
These	O
deviations	B-General_Concept
are	O
called	O
residuals	O
when	O
the	O
calculations	O
are	O
performed	O
over	O
the	O
data	O
sample	O
that	O
was	O
used	O
for	O
estimation	O
and	O
are	O
called	O
errors	O
(	O
or	O
prediction	O
errors	O
)	O
when	O
computed	O
out-of-sample	O
.	O
</s>
<s>
The	O
RMSD	B-General_Concept
serves	O
to	O
aggregate	O
the	O
magnitudes	O
of	O
the	O
errors	O
in	O
predictions	O
for	O
various	O
data	O
points	O
into	O
a	O
single	O
measure	O
of	O
predictive	O
power	O
.	O
</s>
<s>
RMSD	B-General_Concept
is	O
a	O
measure	O
of	O
accuracy	O
,	O
to	O
compare	O
forecasting	O
errors	O
of	O
different	O
models	O
for	O
a	O
particular	O
dataset	O
and	O
not	O
between	O
datasets	O
,	O
as	O
it	O
is	O
scale-dependent	O
.	O
</s>
<s>
RMSD	B-General_Concept
is	O
always	O
non-negative	O
,	O
and	O
a	O
value	O
of	O
0	O
(	O
almost	O
never	O
achieved	O
in	O
practice	O
)	O
would	O
indicate	O
a	O
perfect	O
fit	O
to	O
the	O
data	O
.	O
</s>
<s>
In	O
general	O
,	O
a	O
lower	O
RMSD	B-General_Concept
is	O
better	O
than	O
a	O
higher	O
one	O
.	O
</s>
<s>
RMSD	B-General_Concept
is	O
the	O
square	O
root	O
of	O
the	O
average	O
of	O
squared	O
errors	O
.	O
</s>
<s>
The	O
effect	O
of	O
each	O
error	O
on	O
RMSD	B-General_Concept
is	O
proportional	O
to	O
the	O
size	O
of	O
the	O
squared	O
error	O
;	O
thus	O
larger	O
errors	O
have	O
a	O
disproportionately	O
large	O
effect	O
on	O
RMSD	B-General_Concept
.	O
</s>
<s>
Consequently	O
,	O
RMSD	B-General_Concept
is	O
sensitive	O
to	O
outliers	O
.	O
</s>
<s>
The	O
RMSD	B-General_Concept
of	O
an	O
estimator	O
with	O
respect	O
to	O
an	O
estimated	O
parameter	O
is	O
defined	O
as	O
the	O
square	O
root	O
of	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
:	O
</s>
<s>
For	O
an	O
unbiased	O
estimator	O
,	O
the	O
RMSD	B-General_Concept
is	O
the	O
square	O
root	O
of	O
the	O
variance	O
,	O
known	O
as	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
The	O
RMSD	B-General_Concept
of	O
predicted	O
values	O
for	O
times	O
t	O
of	O
a	O
regression	O
's	O
dependent	O
variable	O
with	O
variables	O
observed	O
over	O
T	O
times	O
,	O
is	O
computed	O
for	O
T	O
different	O
predictions	O
as	O
the	O
square	O
root	O
of	O
the	O
mean	O
of	O
the	O
squares	O
of	O
the	O
deviations	B-General_Concept
:	O
</s>
<s>
(	O
For	O
regressions	O
on	O
cross-sectional	B-General_Concept
data	I-General_Concept
,	O
the	O
subscript	O
t	O
is	O
replaced	O
by	O
i	O
and	O
T	O
is	O
replaced	O
by	O
n	O
.	O
)	O
</s>
<s>
In	O
some	O
disciplines	O
,	O
the	O
RMSD	B-General_Concept
is	O
used	O
to	O
compare	O
differences	O
between	O
two	O
things	O
that	O
may	O
vary	O
,	O
neither	O
of	O
which	O
is	O
accepted	O
as	O
the	O
"	O
standard	O
"	O
.	O
</s>
<s>
Normalizing	O
the	O
RMSD	B-General_Concept
facilitates	O
the	O
comparison	O
between	O
datasets	O
or	O
models	O
with	O
different	O
scales	O
.	O
</s>
<s>
This	O
value	O
is	O
commonly	O
referred	O
to	O
as	O
the	O
normalized	O
root-mean-square	B-General_Concept
deviation	I-General_Concept
or	O
error	O
(	O
NRMSD	B-General_Concept
or	O
NRMSE	O
)	O
,	O
and	O
often	O
expressed	O
as	O
a	O
percentage	O
,	O
where	O
lower	O
values	O
indicate	O
less	O
residual	O
variance	O
.	O
</s>
<s>
Another	O
possible	O
method	O
to	O
make	O
the	O
RMSD	B-General_Concept
a	O
more	O
useful	O
comparison	O
measure	O
is	O
to	O
divide	O
the	O
RMSD	B-General_Concept
by	O
the	O
interquartile	B-General_Concept
range	I-General_Concept
.	O
</s>
<s>
When	O
dividing	O
the	O
RMSD	B-General_Concept
with	O
the	O
IQR	B-General_Concept
the	O
normalized	O
value	O
gets	O
less	O
sensitive	O
for	O
extreme	O
values	O
in	O
the	O
target	O
variable	O
.	O
</s>
<s>
When	O
normalizing	O
by	O
the	O
mean	O
value	O
of	O
the	O
measurements	O
,	O
the	O
term	O
coefficient	O
of	O
variation	O
of	O
the	O
RMSD	B-General_Concept
,	O
CV(RMSD )	O
may	O
be	O
used	O
to	O
avoid	O
ambiguity	O
.	O
</s>
<s>
This	O
is	O
analogous	O
to	O
the	O
coefficient	O
of	O
variation	O
with	O
the	O
RMSD	B-General_Concept
taking	O
the	O
place	O
of	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
Some	O
researchers	O
have	O
recommended	O
the	O
use	O
of	O
the	O
Mean	B-General_Concept
Absolute	I-General_Concept
Error	I-General_Concept
(	O
MAE	O
)	O
instead	O
of	O
the	O
Root	B-General_Concept
Mean	I-General_Concept
Square	I-General_Concept
Deviation	I-General_Concept
.	O
</s>
<s>
MAE	O
possesses	O
advantages	O
in	O
interpretability	O
over	O
RMSD	B-General_Concept
.	O
</s>
<s>
Furthermore	O
,	O
each	O
error	O
influences	O
MAE	O
in	O
direct	O
proportion	O
to	O
the	O
absolute	O
value	O
of	O
the	O
error	O
,	O
which	O
is	O
not	O
the	O
case	O
for	O
RMSD	B-General_Concept
.	O
</s>
<s>
In	O
bioinformatics	O
,	O
the	O
root-mean-square	B-General_Concept
deviation	I-General_Concept
of	O
atomic	O
positions	O
is	O
the	O
measure	O
of	O
the	O
average	O
distance	O
between	O
the	O
atoms	O
of	O
superimposed	O
proteins	O
.	O
</s>
<s>
In	O
structure	O
based	O
drug	O
design	O
,	O
the	O
RMSD	B-General_Concept
is	O
a	O
measure	O
of	O
the	O
difference	O
between	O
a	O
crystal	O
conformation	O
of	O
the	O
ligand	O
conformation	O
and	O
a	O
docking	O
prediction	O
.	O
</s>
<s>
In	O
economics	O
,	O
the	O
RMSD	B-General_Concept
is	O
used	O
to	O
determine	O
whether	O
an	O
economic	O
model	O
fits	O
economic	O
indicators	O
.	O
</s>
<s>
Some	O
experts	O
have	O
argued	O
that	O
RMSD	B-General_Concept
is	O
less	O
reliable	O
than	O
Relative	O
Absolute	O
Error	O
.	O
</s>
<s>
In	O
experimental	O
psychology	O
,	O
the	O
RMSD	B-General_Concept
is	O
used	O
to	O
assess	O
how	O
well	O
mathematical	O
or	O
computational	O
models	O
of	O
behavior	O
explain	O
the	O
empirically	O
observed	O
behavior	O
.	O
</s>
<s>
In	O
GIS	B-Application
,	O
the	O
RMSD	B-General_Concept
is	O
one	O
measure	O
used	O
to	O
assess	O
the	O
accuracy	O
of	O
spatial	O
analysis	O
and	O
remote	O
sensing	O
.	O
</s>
<s>
In	O
hydrogeology	O
,	O
RMSD	B-General_Concept
and	O
NRMSD	B-General_Concept
are	O
used	O
to	O
evaluate	O
the	O
calibration	O
of	O
a	O
groundwater	O
model	O
.	O
</s>
<s>
In	O
imaging	O
science	O
,	O
the	O
RMSD	B-General_Concept
is	O
part	O
of	O
the	O
peak	O
signal-to-noise	O
ratio	O
,	O
a	O
measure	O
used	O
to	O
assess	O
how	O
well	O
a	O
method	O
to	O
reconstruct	O
an	O
image	O
performs	O
relative	O
to	O
the	O
original	O
image	O
.	O
</s>
<s>
In	O
computational	O
neuroscience	O
,	O
the	O
RMSD	B-General_Concept
is	O
used	O
to	O
assess	O
how	O
well	O
a	O
system	O
learns	O
a	O
given	O
model	O
.	O
</s>
<s>
In	O
protein	O
nuclear	O
magnetic	O
resonance	O
spectroscopy	O
,	O
the	O
RMSD	B-General_Concept
is	O
used	O
as	O
a	O
measure	O
to	O
estimate	O
the	O
quality	O
of	O
the	O
obtained	O
bundle	O
of	O
structures	O
.	O
</s>
<s>
Submissions	O
for	O
the	O
Netflix	O
Prize	O
were	O
judged	O
using	O
the	O
RMSD	B-General_Concept
from	O
the	O
test	O
dataset	O
's	O
undisclosed	O
"	O
true	O
"	O
values	O
.	O
</s>
<s>
In	O
the	O
simulation	O
of	O
energy	O
consumption	O
of	O
buildings	O
,	O
the	O
RMSE	B-General_Concept
and	O
CV(RMSE )	O
are	O
used	O
to	O
calibrate	O
models	O
to	O
measured	O
building	O
performance	O
.	O
</s>
<s>
In	O
X-ray	O
crystallography	O
,	O
RMSD	B-General_Concept
(	O
and	O
RMSZ	O
)	O
is	O
used	O
to	O
measure	O
the	O
deviation	B-General_Concept
of	O
the	O
molecular	O
internal	O
coordinates	O
deviate	O
from	O
the	O
restraints	O
library	O
values	O
.	O
</s>
<s>
In	O
control	O
theory	O
,	O
the	O
RMSE	B-General_Concept
is	O
used	O
as	O
a	O
quality	O
measure	O
to	O
evaluate	O
the	O
performance	O
of	O
a	O
State	O
observer	O
.	O
</s>
