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

@inproceedings{Kallioinen2021DetectingAD, title={Detecting and diagnosing prior and likelihood sensitivity with power-scaling}, author={Noa Kallioinen and Topi Paananen and Paul-Christian Burkner and Aki Vehtari}, year={2021} }

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…

## 5 Citations

### Quantification of empirical determinacy: the impact of likelihood weighting on posterior location and spread in Bayesian meta-analysis estimated with JAGS and INLA

- Computer Science
- 2021

This work quantified TED, pEDL and pEDS under different modeling conditions such as model parametrization, the primary outcome, and the prior, and clarified to what extent the location and spread of the marginal posterior distributions of the parameters are determined by the data.

### Prior knowledge elicitation: The past, present, and future

- Computer Science
- 2021

This work analyzes the state of the art of prior elicitation by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert.

### Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy

- Computer Science
- 2022

This work proposes the PAD model taxonomy that defines four basic kinds of Bayesian models, each representing some combination of the assumed joint distribution of all (known or unknown) variables, a posterior approximator (A), and training data (D), and proposes ten utility dimensions according to whichBayesian models can be evaluated holistically.

### A call for changing data analysis practices: from philosophy and comprehensive reporting to modeling approaches and back

- MathematicsPlant and Soil
- 2022

Many applied disciplines have recognized problems related to the practice of data analysis within their own communities. Some of them have even declared the existence of a statistical crisis that has…

## References

SHOWING 1-10 OF 105 REFERENCES

### Sensitivity analysis for Bayesian hierarchical models

- Computer Science
- 2013

This work proposes a novel formal approach to prior sensitivity analysis which quantifies sensitivity without the need for a model re-run, and develops a ready-to-use priorSens package in R which can be used to detect high prior sensitivities of some parameters as well as identifiability issues in possibly over-parametrized Bayesian hierarchical models.

### A weighted strategy to handle likelihood uncertainty in Bayesian inference

- MathematicsComput. Stat.
- 2013

A robust approach is discussed, which allows us to obtain outliers’ resistant posterior distributions with properties similar to those of a proper posterior distribution.

### Confronting Prior Convictions: On Issues of Prior Sensitivity and Likelihood Robustness in Bayesian Analysis

- Mathematics
- 2011

This review explores issues of the sensitivity of Bayes estimates to the prior and form of the likelihood, and a variety of computational strategies for significantly expanding the maintained sampling model, including the use of finite Gaussian mixture models and models based on Dirichlet process priors.

### Bayesian sensitivity analysis with the Fisher–Rao metric

- Mathematics
- 2015

We propose a geometric framework to assess sensitivity of Bayesian procedures to modelling assumptions based on the nonparametric Fisher–Rao metric. While the framework is general, the focus of this…

### Global Robust Bayesian Analysis in Large Models

- EconomicsFederal Reserve Bank of Richmond Working Papers
- 2019

This paper develops tools for global prior sensitivity analysis in large Bayesian models. Without imposing parametric restrictions, the framework provides bounds for a wide range of posterior…

### Sensitivity of a Bayesian Analysis to the Prior Distribution

- MathematicsIEEE Trans. Syst. Man Cybern. Syst.
- 1994

This work describes the sensitivity of a posterior distribution (or posterior mean) to prior and illustrates the results on two distinct problems: a) determining least-informative (vague) priors and b) estimating statistical quantiles for a problem in analyzing projectile accuracy.

### Prior sample size extensions for assessing prior impact and prior‐likelihood discordance

- MathematicsJournal of the Royal Statistical Society: Series B (Statistical Methodology)
- 2014

This paper outlines a framework for quantifying the prior's contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior -likelihood conflict, and develops a simple asymptotic formula for quantification the impact of a proper prior.

### Bayesian estimation - A sensitivity analysis

- Mathematics
- 1975

The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in…