<s>
Particle	B-Algorithm
filters	I-Algorithm
,	O
or	O
sequential	B-Algorithm
Monte	I-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
,	O
are	O
a	O
set	O
of	O
Monte	B-Algorithm
Carlo	I-Algorithm
algorithms	O
used	O
to	O
solve	O
filtering	O
problems	O
arising	O
in	O
signal	O
processing	O
and	O
Bayesian	O
statistical	O
inference	O
.	O
</s>
<s>
The	O
term	O
"	O
particle	B-Algorithm
filters	I-Algorithm
"	O
was	O
first	O
coined	O
in	O
1996	O
by	O
Pierre	O
Del	O
Moral	O
about	O
mean-field	O
interacting	O
particle	O
methods	O
used	O
in	O
fluid	O
mechanics	O
since	O
the	O
beginning	O
of	O
the	O
1960s	O
.	O
</s>
<s>
The	O
term	O
"	O
Sequential	B-Algorithm
Monte	I-Algorithm
Carlo	I-Algorithm
"	O
was	O
coined	O
by	O
Jun	O
S	O
.	O
Liu	O
and	O
Rong	O
Chen	O
in	O
1998	O
.	O
</s>
<s>
Particle	B-Algorithm
filtering	I-Algorithm
uses	O
a	O
set	O
of	O
particles	O
(	O
also	O
called	O
samples	O
)	O
to	O
represent	O
the	O
posterior	O
distribution	O
of	O
a	O
stochastic	O
process	O
given	O
the	O
noisy	O
and/or	O
partial	O
observations	O
.	O
</s>
<s>
Particle	B-Algorithm
filter	I-Algorithm
techniques	O
provide	O
a	O
well-established	O
methodology	O
for	O
generating	O
samples	O
from	O
the	O
required	O
distribution	O
without	O
requiring	O
assumptions	O
about	O
the	O
state-space	O
model	O
or	O
the	O
state	O
distributions	O
.	O
</s>
<s>
Particle	B-Algorithm
filters	I-Algorithm
update	O
their	O
prediction	O
in	O
an	O
approximate	O
(	O
statistical	O
)	O
manner	O
.	O
</s>
<s>
However	O
,	O
it	O
can	O
be	O
mitigated	O
by	O
including	O
a	O
resampling	B-General_Concept
step	O
before	O
the	O
weights	O
become	O
uneven	O
.	O
</s>
<s>
Several	O
adaptive	O
resampling	B-General_Concept
criteria	O
can	O
be	O
used	O
including	O
the	O
variance	O
of	O
the	O
weights	O
and	O
the	O
relative	O
entropy	B-Algorithm
concerning	O
the	O
uniform	O
distribution	O
.	O
</s>
<s>
In	O
the	O
resampling	B-General_Concept
step	O
,	O
the	O
particles	O
with	O
negligible	O
weights	O
are	O
replaced	O
by	O
new	O
particles	O
in	O
the	O
proximity	O
of	O
the	O
particles	O
with	O
higher	O
weights	O
.	O
</s>
<s>
From	O
the	O
statistical	O
and	O
probabilistic	O
point	O
of	O
view	O
,	O
particle	B-Algorithm
filters	I-Algorithm
may	O
be	O
interpreted	O
as	O
mean-field	O
particle	O
interpretations	O
of	O
Feynman-Kac	O
probability	O
measures	O
.	O
</s>
<s>
These	O
particle	O
integration	O
techniques	O
were	O
developed	O
in	O
molecular	O
chemistry	O
and	O
computational	B-Algorithm
physics	I-Algorithm
by	O
Theodore	O
E	O
.	O
Harris	O
and	O
Herman	O
Kahn	O
in	O
1951	O
,	O
Marshall	O
N	O
.	O
Rosenbluth	O
and	O
Arianna	B-Algorithm
W	I-Algorithm
.	I-Algorithm
Rosenbluth	I-Algorithm
in	O
1955	O
,	O
and	O
more	O
recently	O
by	O
Jack	O
H	O
.	O
Hetherington	O
in	O
1984	O
.	O
</s>
<s>
In	O
computational	B-Algorithm
physics	I-Algorithm
,	O
these	O
Feynman-Kac	O
type	O
path	O
particle	O
integration	O
methods	O
are	O
also	O
used	O
in	O
Quantum	O
Monte	B-Algorithm
Carlo	I-Algorithm
,	O
and	O
more	O
specifically	O
Diffusion	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
.	O
</s>
<s>
Feynman-Kac	O
interacting	O
particle	O
methods	O
are	O
also	O
strongly	O
related	O
to	O
mutation-selection	B-Algorithm
genetic	I-Algorithm
algorithms	I-Algorithm
currently	O
used	O
in	O
evolutionary	O
computation	O
to	O
solve	O
complex	O
optimization	O
problems	O
.	O
</s>
<s>
The	O
particle	B-Algorithm
filter	I-Algorithm
methodology	O
is	O
used	O
to	O
solve	O
Hidden	O
Markov	O
Model	O
(	O
HMM	O
)	O
and	O
nonlinear	O
filtering	O
problems	O
.	O
</s>
<s>
With	O
the	O
notable	O
exception	O
of	O
linear-Gaussian	O
signal-observation	O
models	O
(	O
Kalman	O
filter	O
)	O
or	O
wider	O
classes	O
of	O
models	O
(	O
Benes	O
filter	O
)	O
,	O
Mireille	O
Chaleyat-Maurel	O
and	O
Dominique	O
Michel	O
proved	O
in	O
1984	O
that	O
the	O
sequence	O
of	O
posterior	O
distributions	O
of	O
the	O
random	O
states	O
of	O
a	O
signal	O
,	O
given	O
the	O
observations	O
(	O
a.k.a.	O
</s>
<s>
Various	O
other	O
numerical	O
methods	O
based	O
on	O
fixed	O
grid	O
approximations	O
,	O
Markov	B-General_Concept
Chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
techniques	O
,	O
conventional	O
linearization	O
,	O
extended	O
Kalman	O
filters	O
,	O
or	O
determining	O
the	O
best	O
linear	O
system	O
(	O
in	O
the	O
expected	O
cost-error	O
sense	O
)	O
are	O
unable	O
to	O
cope	O
with	O
large-scale	O
systems	O
,	O
unstable	O
processes	O
,	O
or	O
insufficiently	O
smooth	O
nonlinearities	O
.	O
</s>
<s>
Particle	B-Algorithm
filters	I-Algorithm
and	O
Feynman-Kac	O
particle	O
methodologies	O
find	O
application	O
in	O
signal	O
and	O
image	O
processing	O
,	O
Bayesian	O
inference	O
,	O
machine	O
learning	O
,	O
risk	O
analysis	O
and	O
rare	O
event	O
sampling	O
,	O
engineering	O
and	O
robotics	O
,	O
artificial	B-Application
intelligence	I-Application
,	O
bioinformatics	O
,	O
phylogenetics	O
,	O
computational	O
science	O
,	O
economics	O
and	O
mathematical	O
finance	O
,	O
molecular	O
chemistry	O
,	O
computational	B-Algorithm
physics	I-Algorithm
,	O
pharmacokinetics	O
,	O
and	O
other	O
fields	O
.	O
</s>
<s>
From	O
a	O
statistical	O
and	O
probabilistic	O
viewpoint	O
,	O
particle	B-Algorithm
filters	I-Algorithm
belong	O
to	O
the	O
class	O
of	O
branching/genetic	O
type	O
algorithms	O
,	O
and	O
mean-field	O
type	O
interacting	O
particle	O
methodologies	O
.	O
</s>
<s>
Metaheuristic	B-Algorithm
)	O
.	O
</s>
<s>
In	O
computational	B-Algorithm
physics	I-Algorithm
and	O
molecular	O
chemistry	O
,	O
they	O
are	O
used	O
to	O
solve	O
Feynman-Kac	O
path	O
integration	O
problems	O
or	O
to	O
compute	O
Boltzmann-Gibbs	O
measures	O
,	O
top	O
eigenvalues	O
,	O
and	O
ground	O
states	O
of	O
Schrödinger	O
operators	O
.	O
</s>
<s>
The	O
origins	O
of	O
mean-field	O
type	O
evolutionary	B-Algorithm
computational	I-Algorithm
techniques	I-Algorithm
can	O
be	O
traced	O
back	O
to	O
1950	O
and	O
1954	O
with	O
Alan	O
Turing	O
's	O
work	O
on	O
genetic	O
type	O
mutation-selection	O
learning	O
machines	O
and	O
the	O
articles	O
by	O
Nils	O
Aall	O
Barricelli	O
at	O
the	O
Institute	O
for	O
Advanced	O
Study	O
in	O
Princeton	O
,	O
New	O
Jersey	O
.	O
</s>
<s>
The	O
first	O
trace	O
of	O
particle	B-Algorithm
filters	I-Algorithm
in	O
statistical	O
methodology	O
dates	O
back	O
to	O
the	O
mid-1950s	O
;	O
the	O
'	O
Poor	O
Man	O
's	O
Monte	B-Algorithm
Carlo	I-Algorithm
 '	O
,	O
that	O
was	O
proposed	O
by	O
Hammersley	O
et	O
al.	O
,	O
in	O
1954	O
,	O
contained	O
hints	O
of	O
the	O
genetic	O
type	O
particle	B-Algorithm
filtering	I-Algorithm
methods	O
used	O
today	O
.	O
</s>
<s>
Fraser	O
's	O
simulations	O
included	O
all	O
of	O
the	O
essential	O
elements	O
of	O
modern	O
mutation-selection	O
genetic	B-Algorithm
particle	I-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
Quantum	O
Monte	B-Algorithm
Carlo	I-Algorithm
,	O
and	O
more	O
specifically	O
Diffusion	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
can	O
also	O
be	O
interpreted	O
as	O
a	O
mean-field	O
genetic	O
type	O
particle	O
approximation	O
of	O
Feynman-Kac	O
path	O
integrals	O
.	O
</s>
<s>
The	O
origins	O
of	O
Quantum	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
are	O
often	O
attributed	O
to	O
Enrico	O
Fermi	O
and	O
Robert	O
Richtmyer	O
who	O
developed	O
in	O
1948	O
a	O
mean-field	O
particle	O
interpretation	O
of	O
neutron-chain	O
reactions	O
,	O
but	O
the	O
first	O
heuristic-like	O
and	O
genetic	O
type	O
particle	O
algorithm	O
(	O
a.k.a.	O
</s>
<s>
Resampled	O
or	O
Reconfiguration	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
)	O
for	O
estimating	O
ground	O
state	O
energies	O
of	O
quantum	O
systems	O
(	O
in	O
reduced	O
matrix	O
models	O
)	O
is	O
due	O
to	O
Jack	O
H	O
.	O
Hetherington	O
in	O
1984	O
.	O
</s>
<s>
The	O
use	O
of	O
genetic	B-Algorithm
particle	I-Algorithm
algorithms	I-Algorithm
in	O
advanced	O
signal	O
processing	O
and	O
Bayesian	O
inference	O
is	O
more	O
recent	O
.	O
</s>
<s>
In	O
January	O
1993	O
,	O
Genshiro	O
Kitagawa	O
developed	O
a	O
"	O
Monte	B-Algorithm
Carlo	I-Algorithm
filter	O
"	O
,	O
a	O
slightly	O
modified	O
version	O
of	O
this	O
article	O
appeared	O
in	O
1996	O
.	O
</s>
<s>
Independently	O
,	O
the	O
ones	O
by	O
Pierre	O
Del	O
Moral	O
and	O
Himilcon	O
Carvalho	O
,	O
Pierre	O
Del	O
Moral	O
,	O
André	O
Monin	O
,	O
and	O
Gérard	O
Salut	O
on	O
particle	B-Algorithm
filters	I-Algorithm
published	O
in	O
the	O
mid-1990s	O
.	O
</s>
<s>
Particle	B-Algorithm
filters	I-Algorithm
were	O
also	O
developed	O
in	O
signal	O
processing	O
in	O
early	O
1989-1992	O
by	O
P	O
.	O
Del	O
Moral	O
,	O
J.C.	O
Noyer	O
,	O
G	O
.	O
Rigal	O
,	O
and	O
G	O
.	O
Salut	O
in	O
the	O
LAAS-CNRS	O
in	O
a	O
series	O
of	O
restricted	O
and	O
classified	O
research	O
reports	O
with	O
STCAN	O
(	O
Service	O
Technique	O
des	O
Constructions	O
et	O
Armes	O
Navales	O
)	O
,	O
the	O
IT	O
company	O
DIGILOG	O
,	O
and	O
the	O
(	O
the	O
Laboratory	O
for	O
Analysis	O
and	O
Architecture	O
of	O
Systems	O
)	O
on	O
RADAR/SONAR	O
and	O
GPS	O
signal	O
processing	O
problems	O
.	O
</s>
<s>
From	O
1950	O
to	O
1996	O
,	O
all	O
the	O
publications	O
on	O
particle	B-Algorithm
filters	I-Algorithm
,	O
and	O
genetic	B-Algorithm
algorithms	I-Algorithm
,	O
including	O
the	O
pruning	O
and	O
resample	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
introduced	O
in	O
computational	B-Algorithm
physics	I-Algorithm
and	O
molecular	O
chemistry	O
,	O
present	O
natural	O
and	O
heuristic-like	O
algorithms	O
applied	O
to	O
different	O
situations	O
without	O
a	O
single	O
proof	O
of	O
their	O
consistency	O
,	O
nor	O
a	O
discussion	O
on	O
the	O
bias	O
of	O
the	O
estimates	O
and	O
genealogical	O
and	O
ancestral	O
tree-based	O
algorithms	O
.	O
</s>
<s>
The	O
first	O
uniform	O
convergence	O
results	O
concerning	O
the	O
time	O
parameter	O
for	O
particle	B-Algorithm
filters	I-Algorithm
were	O
developed	O
at	O
the	O
end	O
of	O
the	O
1990s	O
by	O
Pierre	O
Del	O
Moral	O
and	O
Alice	O
Guionnet	O
.	O
</s>
<s>
The	O
theory	O
on	O
Feynman-Kac	O
particle	O
methodologies	O
and	O
related	O
particle	B-Algorithm
filter	I-Algorithm
algorithms	O
was	O
developed	O
in	O
2000	O
and	O
2004	O
in	O
the	O
books	O
.	O
</s>
<s>
These	O
abstract	O
probabilistic	O
models	O
encapsulate	O
genetic	B-Algorithm
type	I-Algorithm
algorithms	I-Algorithm
,	O
particle	O
,	O
and	O
bootstrap	O
filters	O
,	O
interacting	O
Kalman	O
filters	O
(	O
a.k.a.	O
</s>
<s>
Rao	O
–	O
Blackwellized	O
particle	B-Algorithm
filter	I-Algorithm
)	O
,	O
importance	B-Algorithm
sampling	I-Algorithm
and	O
resampling	B-General_Concept
style	O
particle	B-Algorithm
filter	I-Algorithm
techniques	O
,	O
including	O
genealogical	O
tree-based	O
and	O
particle	O
backward	O
methodologies	O
for	O
solving	O
filtering	O
and	O
smoothing	O
problems	O
.	O
</s>
<s>
Other	O
classes	O
of	O
particle	B-Algorithm
filtering	I-Algorithm
methodologies	O
include	O
genealogical	O
tree-based	O
models	O
,	O
backward	O
Markov	O
particle	O
models	O
,	O
adaptive	O
mean-field	O
particle	O
models	O
,	O
island-type	O
particle	O
models	O
,	O
and	O
particle	O
Markov	B-General_Concept
chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
methodologies	O
.	O
</s>
<s>
The	O
objective	O
of	O
a	O
particle	B-Algorithm
filter	I-Algorithm
is	O
to	O
estimate	O
the	O
posterior	O
density	O
of	O
the	O
state	O
variables	O
given	O
the	O
observation	O
variables	O
.	O
</s>
<s>
The	O
particle	B-Algorithm
filter	I-Algorithm
is	O
designed	O
for	O
a	O
hidden	O
Markov	O
Model	O
,	O
where	O
the	O
system	O
consists	O
of	O
both	O
hidden	O
and	O
observable	O
variables	O
.	O
</s>
<s>
A	O
generic	O
particle	B-Algorithm
filter	I-Algorithm
estimates	O
the	O
posterior	O
distribution	O
of	O
the	O
hidden	O
states	O
using	O
the	O
observation	O
measurement	O
process	O
.	O
</s>
<s>
The	O
particle	B-Algorithm
filter	I-Algorithm
methodology	O
provides	O
an	O
approximation	O
of	O
these	O
conditional	O
probabilities	O
using	O
the	O
empirical	O
measure	O
associated	O
with	O
a	O
genetic	O
type	O
particle	O
algorithm	O
.	O
</s>
<s>
In	O
contrast	O
,	O
the	O
Markov	B-General_Concept
Chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
or	O
importance	B-Algorithm
sampling	I-Algorithm
approach	O
would	O
model	O
the	O
full	O
posterior	O
.	O
</s>
<s>
If	O
the	O
functions	O
g	O
and	O
h	O
in	O
the	O
above	O
example	O
are	O
linear	O
,	O
and	O
if	O
both	O
and	O
are	O
Gaussian	B-Application
,	O
the	O
Kalman	O
filter	O
finds	O
the	O
exact	O
Bayesian	O
filtering	O
distribution	O
.	O
</s>
<s>
If	O
not	O
,	O
Kalman	O
filter-based	O
methods	O
are	O
a	O
first-order	O
approximation	O
(	O
EKF	O
)	O
or	O
a	O
second-order	O
approximation	O
(	O
UKF	O
in	O
general	O
,	O
but	O
if	O
the	O
probability	O
distribution	O
is	O
Gaussian	B-Application
a	O
third-order	O
approximation	O
is	O
possible	O
)	O
.	O
</s>
<s>
To	O
design	O
a	O
particle	B-Algorithm
filter	I-Algorithm
we	O
simply	O
need	O
to	O
assume	O
that	O
we	O
can	O
sample	O
the	O
transitions	O
of	O
the	O
Markov	O
chain	O
and	O
to	O
compute	O
the	O
likelihood	O
function	O
(	O
see	O
for	O
instance	O
the	O
genetic	O
selection	O
mutation	O
description	O
of	O
the	O
particle	B-Algorithm
filter	I-Algorithm
given	O
below	O
)	O
.	O
</s>
<s>
The	O
particle	B-Algorithm
filter	I-Algorithm
associated	O
with	O
the	O
Markov	O
process	O
given	O
the	O
partial	O
observations	O
is	O
defined	O
in	O
terms	O
of	O
particles	O
evolving	O
in	O
with	O
a	O
likelihood	O
function	O
given	O
with	O
some	O
obvious	O
abusive	O
notation	O
by	O
.	O
</s>
<s>
In	O
the	O
context	O
of	O
particle	B-Algorithm
filters	I-Algorithm
,	O
these	O
ABC	O
particle	B-Algorithm
filtering	I-Algorithm
techniques	O
were	O
introduced	O
in	O
1998	O
by	O
P	O
.	O
Del	O
Moral	O
,	O
J	O
.	O
Jacod	O
and	O
P	O
.	O
Protter	O
.	O
</s>
<s>
Particle	B-Algorithm
filters	I-Algorithm
are	O
also	O
an	O
approximation	O
,	O
but	O
with	O
enough	O
particles	O
they	O
can	O
be	O
much	O
more	O
accurate	O
.	O
</s>
<s>
Feynman-Kac	O
path	O
integration	O
models	O
arise	O
in	O
a	O
variety	O
of	O
scientific	O
disciplines	O
,	O
including	O
in	O
computational	B-Algorithm
physics	I-Algorithm
,	O
biology	O
,	O
information	O
theory	O
and	O
computer	O
sciences	O
.	O
</s>
<s>
In	O
Genetic	B-Algorithm
algorithms	I-Algorithm
and	O
Evolutionary	O
computing	O
community	O
,	O
the	O
mutation-selection	O
Markov	O
chain	O
described	O
above	O
is	O
often	O
called	O
the	O
genetic	B-Algorithm
algorithm	I-Algorithm
with	O
proportional	O
selection	O
.	O
</s>
<s>
The	O
function	O
f	O
,	O
in	O
the	O
usual	O
way	O
for	O
Monte	B-Algorithm
Carlo	I-Algorithm
,	O
can	O
give	O
all	O
the	O
moments	O
etc	O
.	O
</s>
<s>
Particle	B-Algorithm
filters	I-Algorithm
can	O
be	O
interpreted	O
as	O
a	O
genetic	O
type	O
particle	O
algorithm	O
evolving	O
with	O
mutation	O
and	O
selection	O
transitions	O
.	O
</s>
<s>
Particle	B-Algorithm
filters	I-Algorithm
can	O
be	O
interpreted	O
in	O
many	O
different	O
ways	O
.	O
</s>
<s>
The	O
sequential	O
importance	O
resampling	B-General_Concept
technique	O
provides	O
another	O
interpretation	O
of	O
the	O
filtering	O
transitions	O
coupling	O
importance	B-Algorithm
sampling	I-Algorithm
with	O
the	O
bootstrap	B-General_Concept
resampling	I-General_Concept
step	O
.	O
</s>
<s>
Last	O
,	O
but	O
not	O
least	O
,	O
particle	B-Algorithm
filters	I-Algorithm
can	O
be	O
seen	O
as	O
an	O
acceptance-rejection	O
methodology	O
equipped	O
with	O
a	O
recycling	O
mechanism	O
.	O
</s>
<s>
The	O
analysis	O
of	O
the	O
convergence	O
of	O
particle	B-Algorithm
filters	I-Algorithm
was	O
started	O
in	O
1996	O
and	O
in	O
2000	O
in	O
the	O
book	O
and	O
the	O
series	O
of	O
articles	O
.	O
</s>
<s>
Sequential	O
importance	O
Resampling	B-General_Concept
(	O
SIR	O
)	O
,	O
Monte	B-Algorithm
Carlo	I-Algorithm
filtering	O
(	O
Kitagawa	O
1993	O
)	O
and	O
the	O
bootstrap	B-General_Concept
filtering	I-General_Concept
algorithm	O
(	O
Gordon	O
et	O
al	O
.	O
</s>
<s>
Sequential	B-Algorithm
importance	I-Algorithm
sampling	I-Algorithm
(	O
SIS	O
)	O
is	O
a	O
sequential	O
(	O
i.e.	O
,	O
recursive	O
)	O
version	O
of	O
importance	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
The	O
consistency	O
of	O
the	O
resulting	O
particle	B-Algorithm
filter	I-Algorithm
of	O
this	O
approximation	O
and	O
other	O
extensions	O
are	O
developed	O
in	O
.	O
</s>
<s>
Sequential	O
Importance	O
Resampling	B-General_Concept
(	O
SIR	O
)	O
filters	O
with	O
transition	O
prior	O
probability	O
distribution	O
as	O
importance	O
function	O
are	O
commonly	O
known	O
as	O
bootstrap	O
filter	O
and	O
condensation	B-General_Concept
algorithm	I-General_Concept
.	O
</s>
<s>
Resampling	B-General_Concept
is	O
used	O
to	O
avoid	O
the	O
problem	O
of	O
degeneracy	O
of	O
the	O
algorithm	O
,	O
that	O
is	O
,	O
avoiding	O
the	O
situation	O
that	O
all	O
but	O
one	O
of	O
the	O
importance	O
weights	O
are	O
close	O
to	O
zero	O
.	O
</s>
<s>
The	O
performance	O
of	O
the	O
algorithm	O
can	O
be	O
also	O
affected	O
by	O
proper	O
choice	O
of	O
resampling	B-General_Concept
method	O
.	O
</s>
<s>
A	O
single	O
step	O
of	O
sequential	O
importance	O
resampling	B-General_Concept
is	O
as	O
follows	O
:	O
</s>
<s>
5	O
)	O
If	O
the	O
effective	O
number	O
of	O
particles	O
is	O
less	O
than	O
a	O
given	O
threshold	O
,	O
then	O
perform	O
resampling	B-General_Concept
:	O
</s>
<s>
The	O
term	O
"	O
Sampling	O
Importance	O
Resampling	B-General_Concept
"	O
is	O
also	O
sometimes	O
used	O
when	O
referring	O
to	O
SIR	O
filters	O
,	O
but	O
the	O
term	O
Importance	O
Resampling	B-General_Concept
is	O
more	O
accurate	O
because	O
the	O
word	O
"	O
resampling	B-General_Concept
"	O
implies	O
that	O
the	O
initial	O
sampling	O
has	O
already	O
been	O
done	O
.	O
</s>
<s>
Is	O
the	O
same	O
as	O
sequential	O
importance	O
resampling	B-General_Concept
,	O
but	O
without	O
the	O
resampling	B-General_Concept
stage	O
.	O
</s>
<s>
The	O
"	O
direct	O
version	O
"	O
algorithm	O
is	O
rather	O
simple	O
(	O
compared	O
to	O
other	O
particle	B-Algorithm
filtering	I-Algorithm
algorithms	O
)	O
and	O
it	O
uses	O
composition	O
and	O
rejection	O
.	O
</s>
<s>
Particle	B-Algorithm
filters	I-Algorithm
and	O
Feynman-Kac	O
particle	O
methodologies	O
find	O
application	O
in	O
several	O
contexts	O
,	O
as	O
an	O
effective	O
mean	O
for	O
tackling	O
noisy	O
observations	O
or	O
strong	O
nonlinearities	O
,	O
such	O
as	O
:	O
</s>
<s>
pseudo-marginal	B-Algorithm
Metropolis	I-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
