Sequential Monte Carlo in Python
Project description
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 statespace 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.

particle smoothing: fixedlag smoothing, online smoothing, FFBS (forward filtering, backward sampling), twofilter smoothing (O(N) and O(N^2) variants). FFBS for SQMC is also implemented.

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

SMC samplers: SMC tempering, IBIS (a.k.a. data tempering).

Bayesian parameter inference for statespace 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 statespace 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_{t1}
return dists.Normal(loc=xp) # X_t ~ N( X_{t1}, 1)
def PY(self, t, xp, x): # Distribution of Y_t given X_t (and X_{t1})
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 (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.
Project details
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