Detecting and diagnosing prior and likelihood sensitivity with power-scaling

Aug 5, 2026

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Determining how sensitive Bayesian posteriors are to perturbations of the prior and likelihood is central to reliable Bayesian inference. The work introduces a practical, computationally efficient sensitivity analysis method using power-scaling perturbations applied to either the prior or likelihood. A diagnostic is derived to reveal prior-data conflict or likelihood noninformativity. The approach integrates into existing Bayesian workflows with minimal model-builder effort and is implemented in the R package priorsense, demonstrated on real-data case studies.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages21

Reading Time53 min

AccessFree to download

Introduction

Bayesian sensitivity analysis and motivation

Limitations of existing approaches

Power-scaling sensitivity analysis approach

Importance sampling and automated diagnostics

Proposed workflow and figures/tables

View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE [provided by](provided by arXiv.org)[ arXiv.org](provided by arXiv.org) e-Print Archive arXiv :2 107 . 14054v1 [ stat .ME] 29 Jul 2021 Detecting and diagnosing prior and likelihood sensitivity with power-scaling Noa Kallioinen 1 , Topi Paananen 1 , Paul-Christian Bürkner2 , and Aki Vehtari 1 1 Department of Computer Science, Aalto University, Espoo, Finland 2 Cluster of Excellence SimTech, University of Stuttgart, Stuttgart, Germany July 30, 2021 Determining the sensitivity of the posterior to perturbations of the prior and likelihood isan important part of the Bayesian workﬂow. We introduce a practical and computationally eﬃcient sensitivity analysis approach that is applicable to a wide range of models, based on power-scaling perturbations. We suggest a diagnostic based on this that can indicate the presence of prior-data conﬂict or likelihood noninformativity. The approach can be easily included in Bayesian workﬂows with minimal work by the model builder. We present the implementation of the approach in our new R package priorsense and demonstrate the workﬂow on case studies of real data. 1 Introduction Bayesian inference is characterised by the derivation of a posterior from a prior and a likelihood. As the posterior is dependent on the speciﬁcation of these two components, investigating the sensitivity of the posterior to perturbations of the prior and likelihood (sensitivity analysis) is a critical step in the Bayesian workﬂow (Depaoli et al., 2020; Gelman et al., 2020; Lopes & Tobias, 2011) . Along with indicating the robustness of an inference in general, sensitivity is related to issues of prior-data conﬂict (Al Labadi & Evans, 2017; Evans & Moshonov, 2006; Reimherr et al., 2020) and likelihood noninformativity (Gelmanet al., 2017; Poirier, 1998; Roos et al., 2015) . Historically, sensitivity analysis has been an important topic in Bayesian methods research (e.g. Berger, 1990; Berger et al., 1994; Canavos, 1975; Hill & Spall, 1994; Skene et al., 1986) . However, the amount of research on the topic has diminished (Berger et al., 2000; Watson & Holmes, 2016) and results from sensitivity analyses are seldom reported in empirical studies employing Bayesian methods (van de Schoot et al., 2017) . We suggest that one of the main reasons for this is the lack of a sensitivity analysis approach that is easily incorporated into existing modelling workﬂows. Modern modelling workﬂows (e.g. those described in Gelman et al., 2020; Grinsztajn et al., 2021; Schad et al., 2020) generally involve specifying a model in a probabilistic programming language (such as Stan; Stan Development Team, 2021) and using Markov chain Monte Carlo algorithms to approximate the posterior via posterior draws. Reﬁtting a model multiple times this way with diﬀerent perturbations to the prior or likelihood can require substantial amounts of both user and computing time (Jacobi et al., 2018; Pérez et al., 2006) . The use of computationally more eﬃcient methods can reduce the computation time, but existing methods have limitations as they are speciﬁc to particular models (Hunanyan & Roos, 2020) or inference mechanisms (Roos et al. , 2015), require manual speciﬁcation of perturbations (McCartan, 2021), require substantial or technically complex changes to the model code that hinder widespread use (Giordano et al., 2018; Jacobi et al., 2018), or may still require a substantial amount of computation time (Bornn et al., 2010; Ho, 2020) . -5 0 5 10 15 -5 0 5 10 15 -5 0 5 10 15 θ Figure 1 : Example of power-scaling the prior. In this case the prior is normal(0, 2.5) and the likelihood is equivalent to normal(10, 1) . Scaling the prior by raising it to diﬀerent α values (in this case 0.5 and 2.0) changes the posterior (shaded for emphasis), indicating prior sensitivity. In this work, we present an appro

FAQs

What is the main goal of the proposed method?

To provide a computationally efficient sensitivity analysis that diagnoses how posteriors change when the prior or likelihood is power-scaled.

How does power-scaling work in this approach?

The method raises either the prior or the likelihood to an exponent α>0, producing perturbed posteriors whose changes can be quantified and visualized.

What does the diagnostic indicate?

It can indicate the presence of prior-data conflict or likelihood noninformativity, based on the observed pattern of prior and likelihood sensitivity.

Aug 5, 2026

Upload by Jiven