Manifold MCMC for diffusions

Code accompanying the paper Manifold MCMC methods for Bayesian inference in a wide class of diffusion models.

The manifold MCMC methods in the Python package Mici are used for inference, with the sde package in this repository adding some helper functions and classes specific to performing inference in diffusion models.

For a complete example of applying the method described in the paper to perform inference in a Fitzhugh-Nagumo hypoelliptic diffusion model with accompanying explanatory notes see the Jupyter notebook linked below.

FitzHugh-Nagumo_example.ipynb
Open non-interactive version with nbviewer
Open interactive version with Binder
Open interactive version with Google Colab

Local installation

To install the sde package and dependencies to run the notebook locally, first create a local clone of the repository

git clone https://github.com/thiery-lab/manifold-mcmc-for-diffusions.git

Then either create a new Python 3.6+ environment using your environment manager of choice (e.g. conda, virtualenv, venv, pipenv) or activate the existing environment you wish to use.

To install just the sde package and its basic dependencies, from within the manifold-mcmc-for-diffusions directory run

pip install .

To install the sde package plus all the dependencies required to run the example notebook instead run

pip install .[notebook]

Citation

To cite the pre-print the following bibtex entry can be used

@article{graham2019manifold,
  author={Graham, Matthew M. and Thiery, Alexandre H. and Beskos, Alexandros},
  title={Manifold Markov chain Monte Carlo methods for Bayesian inference in a wide class of diffusion models},
  year={2019},
  journal={Pre-print arxiv:1912.02982},
  url={https://arxiv.org/abs/1912.02982}
}