Sequential Monte Carlo in python.

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.

• 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).

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.

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.