# The prior can generally only be understood in the context of the likelihood

arXiv: https://arxiv.org/abs/1708.07487 · HTML: https://mlsanity.com/paper/1708.07487/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2017.

## Built on by (most cited first, 18 of 18)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [LMPriors: Pre-Trained Language Models as Task-Specific Priors](https://mlsanity.com/paper/2210.12530/) (2022)
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- [Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods](https://mlsanity.com/paper/2104.03384/) (2021)
- [On the detrimental effect of invariances in the likelihood for variational inference](https://mlsanity.com/paper/2209.07157/) (2022)
- [Bayesian Neural Networks with Domain Knowledge Priors](https://mlsanity.com/paper/2402.13410/) (2024)
- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Had enough of experts? Quantitative knowledge retrieval from large language models](https://mlsanity.com/paper/2402.07770/) (2024)
- [Graph Structure Learning with Interpretable Bayesian Neural Networks](https://mlsanity.com/paper/2406.14786/) (2024)
- [Posterior SBC: Simulation-Based Calibration Checking Conditional on Data](https://mlsanity.com/paper/2502.03279/) (2025)
- [Informative Bayesian model selection for RR Lyrae star classifiers](https://mlsanity.com/paper/2105.11531/) (2021)
- [Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models](https://mlsanity.com/paper/2308.11672/) (2023)
- [Probabilistic load forecasting with Reservoir Computing](https://mlsanity.com/paper/2308.12844/) (2023)
- [Preferential Normalizing Flows](https://mlsanity.com/paper/2410.08710/) (2024)
- [Expert-elicitation method for non-parametric joint priors using normalizing flows](https://mlsanity.com/paper/2411.15826/) (2024)
- [Bayesian Event-Based Model for Disease Subtype and Stage Inference](https://mlsanity.com/paper/2512.03467/) (2025)
- [Rethinking Likelihood distributions: Student's t Likelihood Boosts Bayesian Neural Network Performance](https://mlsanity.com/paper/2607.25376/) (2026)

## Abstract (arXiv)

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative priors. These methods, however, often manifest a key conceptual tension in prior modeling: a model encoding true prior information should be chosen without reference to the model of the measurement process, but almost all common prior modeling techniques are implicitly motivated by a reference likelihood. In this paper we resolve this apparent paradox by placing the choice of prior into the context of the entire Bayesian analysis, from inference to prediction to model evaluation.