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

2025/07/11 by Bastide, Paul, Estoup, Arnaud, Marin, Jean-Michel +1
#Computation (stat.CO) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2507.08734

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.

Citations

• sbi reloaded: a toolkit for simulation-based inference workflows
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• Neural Density Estimation and Likelihood-free Inference
• Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows
• An efficient likelihood-free Bayesian inference method based on sequential neural posterior estimation
• The Statistical Accuracy of Neural Posterior and Likelihood Estimation