Measuring local sensitivity in Bayesian inference using a new class of metrics

Tabassom Sedighi, Amin Hosseinian-Far, Alireza Daneshkhah

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
7 Downloads (Pure)


The local sensitivity analysis is recognized for its computational simplicity, and potential use in multi-dimensional and complex problems. Unfortunately, its major drawback is its asymptotic behavior where the prior to posterior convergence in terms of the standard metrics (and also computed by Fréchet derivative) used as a local sensitivity measure is not appropriate. The constructed local sensitivity measures do not converge to zero, and even diverge for the most multidimensional classes of prior distributions. Restricting the classes of priors or using other (Formula presented.) -divergence metrics have been proposed as the ways to resolve this issue which were not successful. We overcome this issue, by proposing a new flexible class of metrics so-called credible metrics whose asymptotic behavior is far more promising and no restrictions are required to impose. Using these metrics, the stability of Bayesian inference to the structure of the prior distribution will be then investigated. Under appropriate condition, we present a uniform bound in a sense that a close credible metric a priori will give a close credible metric a posteriori. As a result, we do not get the sort of divergence based on other metrics. We finally show that the posterior predictive distributions are more stable and robust.

Original languageEnglish
Pages (from-to)(In Press)
JournalCommunications in Statistics - Theory and Methods
Volume(In Press)
Early online date16 Sep 2021
Publication statusE-pub ahead of print - 16 Sep 2021

Bibliographical note

© 2022 The Author(s). Published with license by Taylor and Francis Group, LLC
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


  • Bayesian robustness
  • Bayesian stability
  • credible metrics
  • local sensitivity analysis

ASJC Scopus subject areas

  • Statistics and Probability


Dive into the research topics of 'Measuring local sensitivity in Bayesian inference using a new class of metrics'. Together they form a unique fingerprint.

Cite this