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Estimating Marginal Likelihoods in Likelihood-Free Inference via Neural Density Estimation

P Bastide, A Estoup, JM Marin, J Stoehr - arXiv preprint arXiv:2507.08734, 2025 - arxiv.org
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… Crucially, the method is not specific to simulation-based inference and could be applied in any Bayesian setting where a posterior sample is available and a surrogate …

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@article{2507.08734v1,
Author        = {Paul Bastide and Arnaud Estoup and Jean-Michel Marin and Julien Stoehr},
Title         = {Estimating Marginal Likelihoods in Likelihood-Free Inference via Neural Density Estimation},
Eprint        = {2507.08734v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.CO},
Abstract      = {The marginal likelihood, or evidence, plays a central role in Bayesian model selection, yet remains notoriously challenging to compute in likelihood-free settings. While Simulation-Based Inference (SBI) techniques such as Sequential Neural Likelihood Estimation (SNLE) offer powerful tools to approximate posteriors using neural density estimators, they typically do not provide estimates of the evidence. In this technical report presented at BayesComp 2025, we present a simple and general methodology to estimate the marginal likelihood using the output of SNLE.},
Year          = {2025},
Month         = {Jul},
Url           = {http://arxiv.org/abs/2507.08734v1},
File          = {2507.08734v1.pdf}
}

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