# Statisfaction

## particles

Posted in General, Statistics by nicolaschopin on 4 June 2019

I have released a few months ago a Python package for particle filtering, called particles; you can find it on Github here. You may want to have a look first at the documentation, in particular the tutorials here.

This package has been developed to support our (with Omiros Papaspiliopoulos) forthcoming book called (tentatively): an introduction to Sequential Monte Carlo. It implements all the algorithms discussed in the book; e.g.

• bootstrap, guided and auxiliary particle filters
• all standard resampling schemes
• most particle smoothing algorithms
• sequential quasi-Monte Carlo
• PMCMC (PMMH, Particle Gibbs), SMC^2
• SMC samplers

It also contains all the scripts that were used to perform the numerical experiments discussed in the book.

This package is hopefully useful to people with different expectations and level of expertise. For instance, if you just want to run a particle filter for a basic state-space model, you may describe that model as follows:

```import particles
from particles import state_space_models as ssm

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)
```

And then simulate data, and run the corresponding bootstrap filter, as follows:

```my_model = ToySSM(sigma=0.2)
x, y = my_model.simulate(200)  # sample size is 200

alg = particles.SMC(fk=ssm.Bootstrap(ssm=my_model, data=y), N=200)
alg.run()
```

On the other hand, if you are an SMC expert, you may re-use only the parts you need; e.g. a resampling scheme:

```from particles import resampling

A = resampling.systematic(W)
```

Up to now, this package has been tested mostly by my PhD students, and the students of my M2 course on particle filtering at the ENSAE; many thanks to all of them. Since no computer screen has been smashed in the process, I guess I can publicize it a bit more. Please let me know if you have any questions, comments, or feature request. (You may report a bug by raising an issue on the Github page.)

Based on your feedback, I’m planning to write a few more posts in the coming weeks about particles and more generally numerical computation in Python. Stay tuned!

### 4 Responses

1. Pierre Jacob said, on 4 June 2019 at 15:11

Wait, if you’re an SMC expert, why would you use systematic resampling instead of SSP resampling!?

Seriously awesome, Nicolas! Can’t wait to try it out.

• nicolaschopin said, on 4 June 2019 at 15:17

Good point! 🙂

2. Pierre Jacob said, on 5 June 2019 at 01:32

Small typo: the line starting with “y_model” should start with “my_model”, I presume.

• nicolaschopin said, on 5 June 2019 at 15:37

fixed. Thanks!