particles 0.4

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.