harmonic 1.3.1

Python package for efficient Bayesian evidence computation

Python package to efficiently compute the learnt harmonic mean estimator of the Bayesian evidence

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.

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.

Documentation

Comprehensive documentation for harmonic is available.

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.