README.md

Auxiliary Kalman and particle Gibbs samplers for generalised Feynman-Kac models

This is the companion code for the paper Auxiliary MCMC and particle Gibbs samplers for parallelisable inference in latent dynamical systems by Adrien Corenflos and Simo Särkkä.

The models considered here are of the form

$$\pi(x_{0:T}) \propto p_0(x_0) \prod_{t=1}^T p_t(x_t | x_{t-1}) g(x_{0:T})$$

for which the auxiliary Kalman sampler can be implemented as long as $g$ is differentiable and Gaussian approximations of $p_t(x_t | x_{t-1})$ can be computed.

For separable potentials, for example, $g(x_{0:T}) = \prod_{t=0}^T g_t(x_t)$, the second order auxiliary Kalman sampler can be implemented. This is the case for the following models:

$$g(x_{0:T}) = \prod_{t=0}^T g_t(x_t) = \prod_{t=0}^T p(y_t | x_t)$$

Particle Gibbs samplers can be implemented for models of the form

$$\pi(x_{0:T}) \propto p_0(x_0)g_0(x_0) \prod_{t=1}^T p_t(x_t | x_{t-1}) g(x_t, x_{t-1}).$$

When $p_t(x_t | x_{t-1})$ is approximated by a Gaussian, and/or when $g$ is differentiable, improvements can be achieved as explained in the paper.

To install this, be sure to follow the official JAX installation instructions, and then run

    pip install -e .

or any other way of installing a Python package from source of your preference.

Examples can be found in the examples folder, together with scripts to reproduce the results described in the paper.