<s>
In	O
computational	B-Algorithm
statistics	I-Algorithm
,	O
the	O
pseudo-marginal	B-Algorithm
Metropolis	I-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
to	O
sample	O
from	O
a	O
probability	O
distribution	O
.	O
</s>
<s>
It	O
is	O
an	O
instance	O
of	O
the	O
popular	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
that	O
extends	O
its	O
use	O
to	O
cases	O
where	O
the	O
target	O
density	O
is	O
not	O
available	O
analytically	O
.	O
</s>
<s>
It	O
relies	O
on	O
the	O
fact	O
that	O
the	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
can	O
still	O
sample	O
from	O
the	O
correct	O
target	O
distribution	O
if	O
the	O
target	O
density	O
in	O
the	O
acceptance	O
ratio	O
is	O
replaced	O
by	O
an	O
estimate	O
.	O
</s>
<s>
The	O
algorithm	O
follows	O
the	O
same	O
steps	O
as	O
the	O
standard	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
except	O
that	O
the	O
evaluation	O
of	O
the	O
target	O
density	O
is	O
replaced	O
by	O
a	O
non-negative	O
and	O
unbiased	O
estimate	O
.	O
</s>
<s>
For	O
comparison	O
,	O
the	O
main	O
steps	O
of	O
a	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
are	O
outlined	O
below	O
.	O
</s>
<s>
Given	O
a	O
current	O
state	O
the	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
proposes	O
a	O
new	O
state	O
according	O
to	O
some	O
density	O
.	O
</s>
<s>
The	O
pseudo-marginal	B-Algorithm
Metropolis	I-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
in	O
contrast	O
only	O
assumes	O
the	O
existence	O
of	O
an	O
unbiased	O
estimator	O
,	O
i.e.	O
</s>
<s>
Since	O
there	O
is	O
often	O
no	O
analytic	O
expression	O
of	O
this	O
quantity	O
,	O
one	O
often	O
relies	O
on	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
to	O
sample	O
from	O
the	O
distribution	O
instead	O
.	O
</s>
<s>
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
often	O
need	O
the	O
likelihood	O
to	O
be	O
accessible	O
for	O
every	O
parameter	O
value	O
.	O
</s>
<s>
Pseudo-marginal	O
Metropolis-Hastings	B-Algorithm
can	O
be	O
seen	O
as	O
a	O
special	O
case	O
of	O
so-called	O
particle	O
marginal	O
Metropolis-Hastings	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
In	O
the	O
case	O
of	O
the	O
latter	O
,	O
unbiased	O
estimators	O
of	O
densities	O
relating	O
to	O
static	O
parameters	O
in	O
state-space	O
models	O
may	O
be	O
obtained	O
using	O
a	O
particle	B-Algorithm
filter	I-Algorithm
.	O
</s>
