<s>
In	O
computational	B-Algorithm
statistics	I-Algorithm
,	O
the	O
preconditioned	B-Algorithm
Crank	I-Algorithm
–	I-Algorithm
Nicolson	I-Algorithm
algorithm	I-Algorithm
(	O
pCN	O
)	O
is	O
a	O
Markov	B-General_Concept
chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
(	O
MCMC	O
)	O
method	O
for	O
obtaining	O
random	B-Algorithm
samples	I-Algorithm
–	O
sequences	O
of	O
random	O
observations	O
–	O
from	O
a	O
target	O
probability	O
distribution	O
for	O
which	O
direct	O
sampling	O
is	O
difficult	O
.	O
</s>
<s>
The	O
most	O
significant	O
feature	O
of	O
the	O
pCN	B-Algorithm
algorithm	I-Algorithm
is	O
its	O
dimension	O
robustness	O
,	O
which	O
makes	O
it	O
well-suited	O
for	O
high-dimensional	O
sampling	O
problems	O
.	O
</s>
<s>
The	O
pCN	B-Algorithm
algorithm	I-Algorithm
is	O
well-defined	O
,	O
with	O
non-degenerate	O
acceptance	O
probability	O
,	O
even	O
for	O
target	O
distributions	O
on	O
infinite-dimensional	O
Hilbert	O
spaces	O
.	O
</s>
<s>
on	O
an	O
N-dimensional	O
subspace	O
of	O
the	O
original	O
Hilbert	O
space	O
,	O
the	O
convergence	O
properties	O
(	O
such	O
as	O
ergodicity	O
)	O
of	O
the	O
algorithm	O
are	O
independent	O
of	O
N	O
.	O
This	O
is	O
in	O
strong	O
contrast	O
to	O
schemes	O
such	O
as	O
Gaussian	O
random	O
walk	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
and	O
the	O
Metropolis-adjusted	B-Algorithm
Langevin	I-Algorithm
algorithm	I-Algorithm
,	O
whose	O
acceptance	O
probability	O
degenerates	O
to	O
zero	O
as	O
N	O
tends	O
to	O
infinity	O
.	O
</s>
<s>
The	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
general	O
class	O
of	O
methods	O
that	O
try	O
to	O
produce	O
such	O
Markov	O
chains	O
,	O
and	O
do	O
so	O
by	O
a	O
two-step	O
procedure	O
of	O
first	O
proposing	O
a	O
new	O
state	O
given	O
the	O
current	O
state	O
and	O
then	O
accepting	O
or	O
rejecting	O
this	O
proposal	O
,	O
according	O
to	O
a	O
particular	O
acceptance	O
probability	O
,	O
to	O
define	O
the	O
next	O
state	O
.	O
</s>
<s>
The	O
idea	O
of	O
the	O
pCN	B-Algorithm
algorithm	I-Algorithm
is	O
that	O
a	O
clever	O
choice	O
of	O
(	O
non-symmetric	O
)	O
proposal	O
for	O
a	O
new	O
state	O
given	O
might	O
have	O
an	O
associated	O
acceptance	O
probability	O
function	O
with	O
very	O
desirable	O
properties	O
.	O
</s>
