<s>
In	O
Bayesian	O
inference	O
,	O
the	O
Bernstein	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
theorem	I-General_Concept
provides	O
the	O
basis	O
for	O
using	O
Bayesian	O
credible	O
sets	O
for	O
confidence	O
statements	O
in	O
parametric	B-General_Concept
models	I-General_Concept
.	O
</s>
<s>
The	O
Bernstein	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
theorem	I-General_Concept
links	O
Bayesian	O
inference	O
with	O
frequentist	B-General_Concept
inference	I-General_Concept
.	O
</s>
<s>
In	O
case	O
the	O
maximum	O
likelihood	O
estimator	O
is	O
an	O
efficient	O
estimator	O
,	O
we	O
can	O
plug	O
this	O
in	O
,	O
and	O
we	O
recover	O
a	O
common	O
,	O
more	O
specific	O
,	O
version	O
of	O
the	O
Bernstein	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
theorem	I-General_Concept
.	O
</s>
<s>
The	O
most	O
important	O
implication	O
of	O
the	O
Bernstein	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
theorem	I-General_Concept
is	O
that	O
the	O
Bayesian	O
inference	O
is	O
asymptotically	O
correct	O
from	O
a	O
frequentist	B-General_Concept
point	O
of	O
view	O
.	O
</s>
<s>
This	O
means	O
that	O
for	O
large	O
amounts	O
of	O
data	O
,	O
one	O
can	O
use	O
the	O
posterior	O
distribution	O
to	O
make	O
,	O
from	O
a	O
frequentist	B-General_Concept
point	O
of	O
view	O
,	O
valid	O
statements	O
about	O
estimation	O
and	O
uncertainty	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
nonparametric	O
statistics	O
,	O
the	O
Bernstein	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
theorem	I-General_Concept
usually	O
fails	O
to	O
hold	O
with	O
a	O
notable	O
exception	O
of	O
the	O
Dirichlet	B-General_Concept
process	I-General_Concept
.	O
</s>
<s>
A	O
remarkable	O
result	O
was	O
found	O
by	O
Freedman	O
in	O
1965	O
:	O
the	O
Bernstein	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
theorem	I-General_Concept
does	O
not	O
hold	O
almost	O
surely	O
if	O
the	O
random	O
variable	O
has	O
an	O
infinite	O
countable	O
probability	O
space	O
;	O
however	O
,	O
this	O
depends	O
on	O
allowing	O
a	O
very	O
broad	O
range	O
of	O
possible	O
priors	O
.	O
</s>
