particles 0.4

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Description:

particles 0.4

particles
Sequential Monte Carlo in python.
Motivation
This package was developed to complement the following book:
An introduction to Sequential Monte Carlo
by Nicolas Chopin and Omiros Papaspiliopoulos.
It now also implements algorithms and methods introduced after the book was
published, see below.
Features


particle filtering: bootstrap filter, guided filter, APF.


resampling: multinomial, residual, stratified, systematic and SSP.


possibility to define state-space models using some (basic) form of
probabilistic programming; see below for an example.


SQMC (Sequential quasi Monte Carlo); routines for computing the Hilbert curve,
and generating RQMC sequences.


FFBS (forward filtering backward sampling): standard, O(N^2) variant, and
faster variants based on either MCMC, pure rejection, or the hybrid scheme;
see Dau & Chopin (2022) for a discussion. The QMC version of Gerber and
Chopin (2017, Bernoulli) is also implemented.


other smoothing algorithms: fixed-lag smoothing, on-line smoothing,
two-filter smoothing (O(N) and O(N^2) variants).


Exact filtering/smoothing algorithms: Kalman (for linear Gaussian models)
and forward-backward recursions (for finite hidden Markov models).


Standard and waste-free SMC samplers: SMC tempering, IBIS (a.k.a. data
tempering). SMC samplers for binary words (Schäfer and Chopin, 2014), with
application to variable selection.


Bayesian parameter inference for state-space models: PMCMC (PMMH, Particle Gibbs)
and SMC^2.


Basic support for parallel computation (i.e. running multiple SMC algorithms
on different CPU cores).


Variance estimators (Chan and Lai, 2013 ; Lee and Whiteley, 2018; Olsson
and Douc, 2019).


nested sampling: both the vanilla version and the SMC sampler of Salomone
et al (2018).


Example
Here is how you may define a parametric state-space model:
import particles
import particles.state_space_models as ssm
import particles.distributions as dists

class ToySSM(ssm.StateSpaceModel):
def PX0(self): # Distribution of X_0
return dists.Normal() # X_0 ~ N(0, 1)
def PX(self, t, xp): # Distribution of X_t given X_{t-1}
return dists.Normal(loc=xp) # X_t ~ N( X_{t-1}, 1)
def PY(self, t, xp, x): # Distribution of Y_t given X_t (and X_{t-1})
return dists.Normal(loc=x, scale=self.sigma) # Y_t ~ N(X_t, sigma^2)

You may now choose a particular model within this class, and simulate data from it:
my_model = ToySSM(sigma=0.2)
x, y = my_model.simulate(200) # sample size is 200

To run a bootstrap particle filter for this model and data y, simply do:
alg = particles.SMC(fk=ssm.Bootstrap(ssm=my_model, data=y), N=200)
alg.run()

That's it! Head to the
documentation
for more examples, explanations, and installation instructions.
Who do I talk to?
Nicolas Chopin ([email protected]) is the main author, contributor, and
person to blame if things do not work as expected.
Bug reports, feature requests, questions, rants, etc are welcome, preferably
on the github page.

License

For personal and professional use. You cannot resell or redistribute these repositories in their original state.

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