Welcome to beetroots’s documentation!
Beetroots (BayEsian infErence with spaTial Regularization of nOisy multi-line ObservaTion mapS) is a Python package that performs Bayesian inference of physical parameters from multispectral-structured cubes with a dedicated sampling algorithm. Thanks to this sampling algorithm, beetroots provides maps of credibility intervals along with estimated maps.
The sampling algorithm is introduced in
Palud, P.-A. Thouvenin, P. Chainais, E. Bron, and F. Le Petit - Efficient sampling of non log-concave posterior distributions with mixture of noises, IEEE Transactions on Signal Processing, vol. 71, pp. 2491 – 2501, 2023. DOI: 10.1109/TSP.2023.3289728
Such inversions rely on a forward model that is assumed to emulate accurately the physics of the observed environment. In parallel of the inversion, beetroots tests this hypothesis to evaluate the validity of the inference results. The testing method is described in (in French)
Palud, P. Chainais, F. Le Petit, P.-A. Thouvenin and E. Bron - Problèmes inverses et test bayésien d’adéquation du modèle, GRETSI - Groupe de Recherche en Traitement du Signal et des Images in 29e Colloque sur le traitement du signal et des images, Grenoble, pp. 705 – 708, 2023.
This package was applied e.g., to infer physical conditions in different regions of the interstellar medium in
Palud, P.-A. Thouvenin, P. Chainais, E. Bron, F. Le Petit and ORION-B consortium - Bayesian inversion of large interstellar medium observation maps, in prep
It was also exploited to assert and compare the relevance of tracers and combination of tracers to constrain physical conditions in
Einig, P. Palud, A. Roueff, P.-A. Thouvenin, P. Chainais, E. Bron, F. Le Petit, J. Pety, J. Chanussot and ORION-B consortium - Entropy-based selection of most informative observables for inference from interstellar medium observations, in prep
Note
Astrophysics applications rely on a neural network-based approximation of the forward model for
faster evaluation
ability to evaluate derivatives
The package used to derive this approximation is nnbma (Neural Network-Based Model Approximation). Here are the links towards the corresponding GitHub repository, PyPi package and documentation. The paper presenting this package is
Palud, L. Einig, F. Le Petit, E. Bron, P. Chainais, J. Chanussot, J. Pety, P.-A. Thouvenin and ORION-B consortium - Neural network-based emulation of interstellar medium models, Astronomy & Astrophysics, 2023, 678, pp.A198. DOI: 10.1051/0004-6361/202347074
Installation
To prepare and perform an inversion, we recommend installing the package.
The package can be installed with pip:
pip install beetroots
or by cloning the repo. To clone, install and test the package, run:
git clone git@github.com:pierrePalud/beetroots.git
cd beetroots
poetry install # or poetry install -E notebook -E docs for extra dependencies
poetry shell
pytest
Package structure and how to adapt it to your use cases
This package is large and contains a lot of python modules. To facilitate code exploration and use, here is an un-rigorous UML class diagram of the code:
The examples in the Gallery of examples clarify the package structure and in particular what the user needs to interact with. This diagram is maintained here for completeness.
Contents
Indices and tables
References
Here are the references used throughout this documentation:
Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. Bayesian Data Analysis. Chapman and Hall/CRC, 3 edition, 2015. ISBN 978-0-429-11307-9. doi:10.1201/b16018.
A.T. Ihler, J.W. Fisher, R.L. Moses, and A.S. Willsky. Nonparametric belief propagation for self-localization of sensor networks. IEEE Journal on Selected Areas in Communications, 23(4):809–819, 2005. doi:10.1109/JSAC.2005.843548.
C. Joblin, E. Bron, C. Pinto, P. Pilleri, F. Le Petit, M. Gerin, J. Le Bourlot, A. Fuente, O. Berne, J. R. Goicoechea, E. Habart, M. Köhler, D. Teyssier, Z. Nagy, J. Montillaud, C. Vastel, J. Cernicharo, M. Röllig, V. Ossenkopf-Okada, and E. A. Bergin. Structure of photodissociation fronts in star-forming regions revealed by \emph Herschel observations of high-J CO emission lines. A&A, 615:A129, 2018. doi:10.1051/0004-6361/201832611.
Martina Nardon and Paolo Pianca. Simulation techniques for generalized Gaussian densities. Journal of Statistical Computation and Simulation, 79(11):1317–1329, 2009. doi:10.1080/00949650802290912.
P. Palud, P. Chainais, F. Le Petit, P.-A. Thouvenin, and E. Bron. Problèmes inverses et test bayésien d'adéquation du modèle. In 29° Colloque sur le traitement du signal et des images, p. 705–708. GRETSI - Groupe de Recherche en Traitement du Signal et des Images, 2023.
P. Palud, L. Einig, F. Le Petit, E. Bron, P. Chainais, J. Chanussot, J. Pety, P.-A. Thouvenin, D. Languignon, I. Beslić, M. Garcia Santa-Maria, J.H. Orkisz, L. Ségal, A. Zakardjian, S. Bardeau, M. Gerin, J.R. Goicoechea, P. Gratier, V.V. Guzman, and et al. Neural network-based emulation of interstellar medium models. A&A, 2023. doi:10.1051/0004-6361/202347074.
P. Palud, P.-A. Thouvenin, P. Chainais, E. Bron, and F. Le Petit. Efficient sampling of non log-concave posterior distributions with mixture of noises. IEEE Transactions on Signal Processing, 71:2491–2501, 2023. doi:10.1109/TSP.2023.3289728.
Ana F. Vidal, Valentin De Bortoli, Marcelo Pereyra, and Alain Durmus. Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part I: Methodology and Experiments. 2020. URL: http://arxiv.org/abs/1911.11709 (visited on 2022-07-20), arXiv:1911.11709.