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Savage-Dickey density ratio estimation with normalizing flows for Bayesian model comparison

K Lin, A Polanska, D Piras, AS Mancini… - arXiv preprint arXiv …, 2025 - arxiv.org
Astrophysics paper astro-ph.CO Suggest

… calculated with the learned harmonic mean or with nested sampling directly for the BHM setting, we validate our results by comparison with a simulation-based inference (…

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BibTeX

@article{2506.04339v1,
Author        = {Kiyam Lin and Alicja Polanska and Davide Piras and Alessio Spurio Mancini and Jason D. McEwen},
Title         = {Savage-Dickey density ratio estimation with normalizing flows for
  Bayesian model comparison},
Eprint        = {2506.04339v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {astro-ph.CO},
Abstract      = {A core motivation of science is to evaluate which scientific model best
explains observed data. Bayesian model comparison provides a principled
statistical approach to comparing scientific models and has found widespread
application within cosmology and astrophysics. Calculating the Bayesian
evidence is computationally challenging, especially as we continue to explore
increasingly more complex models. The Savage-Dickey density ratio (SDDR)
provides a method to calculate the Bayes factor (evidence ratio) between two
nested models using only posterior samples from the super model. The SDDR
requires the calculation of a normalised marginal distribution over the extra
parameters of the super model, which has typically been performed using
classical density estimators, such as histograms. Classical density estimators,
however, can struggle to scale to high-dimensional settings. We introduce a
neural SDDR approach using normalizing flows that can scale to settings where
the super model contains a large number of extra parameters. We demonstrate the
effectiveness of this neural SDDR methodology applied to both toy and realistic
cosmological examples. For a field-level inference setting, we show that Bayes
factors computed for a Bayesian hierarchical model (BHM) and simulation-based
inference (SBI) approach are consistent, providing further validation that SBI
extracts as much cosmological information from the field as the BHM approach.
The SDDR estimator with normalizing flows is implemented in the open-source
harmonic Python package.},
Year          = {2025},
Month         = {Jun},
Url           = {http://arxiv.org/abs/2506.04339v1},
File          = {2506.04339v1.pdf}
}

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