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harmonic is an open source, well tested and documented Python implementation of the learnt harmonic mean estimator (McEwen et al. 2021) to compute the marginal likelihood (Bayesian evidence), required for Bayesian model selection.

For an accessible overview of the learnt harmonic mean estimator please see this Towards Data Science article.

While harmonic requires only posterior samples, and so is agnostic to the technique used to perform Markov chain Monte Carlo (MCMC) sampling, harmonic works well with MCMC sampling techniques that naturally provide samples from multiple chains by their ensemble nature, such as affine invariant ensemble samplers. For instance, harmonic can be used with the popular emcee code implementing the affine invariant sampler of Goodman & Weare (2010), or the NumPyro code implementing various MCMC algorithms.

Basic usage is highlighted in this interactive demo.

Overview video

Installation

Brief installation instructions are given below (for further details see the full installation documentation).

Quick install (PyPi)

The harmonic package can be installed by running

pip install harmonic

Install from source (GitHub)

The harmonic package can also be installed from source by running

git clone https://github.com/astro-informatics/harmonic
cd harmonic

and installing within the root directory, with one command

pip install .

To check the install has worked correctly run the unit tests with

pytest

To build the documentation from source run

cd docs && make html

Then open ./docs/_build/html/index.html in a browser.

Documentation

Comprehensive documentation for harmonic is available.

Contributors

Jason D. McEwen, Christopher G. R. Wallis, Matthew A. Price, Matthew M. Docherty, Alessio Spurio Mancini, Alicja Polanska.

Attribution

Please cite McEwen et al. (2021) if this code package has been of use in your project.

A BibTeX entry for the paper is:

@article{harmonic,
   author = {Jason~D.~McEwen and Christopher~G.~R.~Wallis and Matthew~A.~Price and Matthew~M.~Docherty},
    title = {Machine learning assisted {B}ayesian model comparison: learnt harmonic mean estimator},
  journal = {ArXiv},
   eprint = {arXiv:2111.12720},
     year = 2021
}

Please also cite Polanska et al. (2024) if using normalizing flow models.

A BibTeX entry for the paper is:

@misc{polanska2024learned,
    title={Learned harmonic mean estimation of the Bayesian evidence with normalizing flows},
    author={Alicja Polanska and Matthew A. Price and Davide Piras and Alessio Spurio Mancini and Jason D. McEwen},
    year={2024},
    eprint={2405.05969},
    archivePrefix={arXiv},
    primaryClass={astro-ph.IM}
}

Please also cite Spurio Mancini et al. (2022) if this code has been of use in a simulation-based inference project.

A BibTeX entry for the paper is:

@article{spurio-mancini:harmonic_sbi,
   author   = {A.~Spurio Mancini and M.~M.~Docherty and M.~A.~Price and J.~D.~McEwen},
   doi      = {10.1093/rasti/rzad051},
   eprint   = {arXiv:2207.04037},
   journal  = {{RASTI}, in press},
   title    = {{B}ayesian model comparison for simulation-based inference},
   year     = {2023}
}

License

harmonic is released under the GPL-3 license (see LICENSE.txt), subject to the non-commercial use condition (see LICENSE_EXT.txt)

harmonic
Copyright (C) 2021 Jason D. McEwen, Christopher G. R. Wallis,
Matthew A. Price, Matthew M. Docherty, Alessio Spurio Mancini,
Alicja Polanska & contributors

This program is released under the GPL-3 license (see LICENSE.txt),
subject to a non-commercial use condition (see LICENSE_EXT.txt).

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.