You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
``harmonic`` is an open source, well tested and documented Python implementation of the *learnt harmonic mean estimator* (`McEwen et al. 2021 <https://arxiv.org/abs/2111.12720>`_) to compute the marginal likelihood (Bayesian evidence), required for Bayesian model selection.
37
+
``harmonic`` is an open source, well tested and documented Python implementation of the *learned harmonic mean estimator* (`McEwen et al. 2021 <https://arxiv.org/abs/2111.12720>`_) to compute the marginal likelihood (Bayesian evidence), required for Bayesian model selection.
34
38
35
-
For an accessible overview of the *learnt harmonic mean estimator* please see this `Towards Data Science article <https://towardsdatascience.com/learnt-harmonic-mean-estimator-for-bayesian-model-selection-47258bb0fc2e>`_.
39
+
For an accessible overview of the *learned harmonic mean estimator* please see this `Towards Data Science article <https://towardsdatascience.com/learnt-harmonic-mean-estimator-for-bayesian-model-selection-47258bb0fc2e>`_.
36
40
37
41
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 <https://github.com/dfm/emcee>`_ code implementing the affine invariant sampler of `Goodman & Weare (2010) <https://cims.nyu.edu/~weare/papers/d13.pdf>`_, or the `NumPyro <https://github.com/pyro-ppl/numpyro>`_ code implementing various MCMC algorithms.
38
42
@@ -146,6 +150,22 @@ A BibTeX entry for the paper is:
146
150
year = {2023}
147
151
}
148
152
153
+
Please *also* cite `Lin et al. (2025) <https://arxiv.org/abs/2506.04339>`_ if using the Savage-Dickey density ratio estimation.
154
+
155
+
A BibTeX entry for the paper is:
156
+
157
+
.. code-block::
158
+
159
+
@article{spurio-mancini:harmonic_sddr,
160
+
title={{S}avage-{D}ickey density ratio estimation with normalizing flows for {B}ayesian model comparison},
161
+
author={Kiyam Lin and Alicja Polanska and Davide Piras and Alessio Spurio Mancini and Jason D. McEwen},
0 commit comments