# Detecting and diagnosing prior and likelihood sensitivity with power-scaling

arXiv: https://arxiv.org/abs/2107.14054 · HTML: https://mlsanity.com/paper/2107.14054/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2021.

## Built on by (most cited first, 7 of 7)

- [Sensitivity-Aware Amortized Bayesian Inference](https://mlsanity.com/paper/2310.11122/) (2023)
- [Conditional Bayesian Quadrature](https://mlsanity.com/paper/2406.16530/) (2024)
- [Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference](https://mlsanity.com/paper/2312.05153/) (2023)
- [Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework](https://mlsanity.com/paper/2502.00846/) (2025)
- [Power-scaled Bayesian Inference with Score-based Generative Models](https://mlsanity.com/paper/2504.10807/) (2025)
- [A Practitioner's Guide to Bayesian Inference in Pharmacometrics using Pumas](https://mlsanity.com/paper/2304.04752/) (2023)
- [Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy](https://mlsanity.com/paper/2412.11875/) (2024)

## Abstract (arXiv)

Determining the sensitivity of the posterior to perturbations of the prior and likelihood is an important part of the Bayesian workflow. We introduce a practical and computationally efficient sensitivity analysis approach using importance sampling to estimate properties of posteriors resulting from power-scaling the prior or likelihood. On this basis, we suggest a diagnostic that can indicate the presence of prior-data conflict or likelihood noninformativity and discuss limitations to this power-scaling approach. The approach can be easily included in Bayesian workflows with minimal effort by the model builder and we present an implementation in our new R package priorsense. We further demonstrate the workflow on case studies of real data using models varying in complexity from simple linear models to Gaussian process models.