# Bayesian Evidence and Model Selection

arXiv: https://arxiv.org/abs/1411.3013 · HTML: https://mlsanity.com/paper/1411.3013/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2014.

## Built on by (most cited first, 12 of 12)

- [LogME: Practical Assessment of Pre-trained Models for Transfer Learning](https://mlsanity.com/paper/2102.11005/) (2021)
- [Ranking and Tuning Pre-trained Models: A New Paradigm for Exploiting Model Hubs](https://mlsanity.com/paper/2110.10545/) (2021)
- [Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison](https://mlsanity.com/paper/2305.11241/) (2023)
- [Improving the Accuracy of Amortized Model Comparison with Self-Consistency](https://mlsanity.com/paper/2508.20614/) (2025)
- [On the safe use of prior densities for Bayesian model selection](https://mlsanity.com/paper/2206.05210/) (2022)
- [Differentiable Annealed Importance Sampling Minimizes The Symmetrized Kullback-Leibler Divergence Between Initial and Target Distribution](https://mlsanity.com/paper/2405.14840/) (2024)
- [Towards fast machine-learning-assisted Bayesian posterior inference of microseismic event location and source mechanism](https://mlsanity.com/paper/2101.04724/) (2021)
- [KITE: A Kernel-based Improved Transferability Estimation Method](https://mlsanity.com/paper/2405.01603/) (2024)
- [Causal, Bayesian, & Non-parametric Modeling of the SARS-CoV-2 Viral Load Distribution vs. Patient's Age](https://mlsanity.com/paper/2105.13483/) (2021)
- [Improved identification accuracy in equation learning via comprehensive boldsymbolR2-elimination and Bayesian model selection](https://mlsanity.com/paper/2311.13265/) (2023)
- [Efficient Transferability Assessment for Selection of Pre-trained Detectors](https://mlsanity.com/paper/2403.09432/) (2024)
- [Nested Sampling: A Critical and Comprehensive Theoretical Guide](https://mlsanity.com/paper/2606.17916/) (2026)

## Abstract (arXiv)

In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical techniques. Specific attention is paid to the Laplace approximation, variational Bayes, importance sampling, thermodynamic integration, and nested sampling and its recent variants. Analogies to statistical physics, from which many of these techniques originate, are discussed in order to provide readers with deeper insights that may lead to new techniques. The utility of Bayesian model testing in the domain sciences is demonstrated by presenting four specific practical examples considered within the context of signal processing in the areas of signal detection, sensor characterization, scientific model selection and molecular force characterization.