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.

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 (basic, experimental).

Example

Here is how you may define a parametric state-space model:

```python import particles import particles.statespacemodels as ssm import particles.distributions as dists

class ToySSM(ssm.StateSpaceModel): def PX0(self): # Distribution of X0 return dists.Normal() # X0 ~ N(0, 1) def PX(self, t, xp): # Distribution of Xt given X{t-1} return dists.Normal(loc=xp) # Xt ~ N( X{t-1}, 1) def PY(self, t, xp, x): # Distribution of Yt given Xt (and X{t-1}) return dists.Normal(loc=x, scale=self.sigma) # Yt ~ N(X_t, sigma^2) ```

You may now choose a particular model within this class, and simulate data from it:

python 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:

python 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 (nicolas.chopin@ensae.fr) 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.