Sensitivity analysis for Bayesian hierarchical models

Małgorzata Roos, Thiago G. Martins, Leonhard Held, Haavard Rue

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

Prior sensitivity examination plays an important role in applied Bayesian analyses. This is especially true for Bayesian hierarchical models, where interpretability of the parameters within deeper layers in the hierarchy becomes challenging. In addition, lack of information together with identifiability issues may imply that the prior distributions for such models have an undesired influence on the posterior inference. Despite its importance, informal approaches to prior sensitivity analysis are currently used. They require repetitive re-fits of the model with ad-hoc modified base prior parameter values. Other formal approaches to prior sensitivity analysis suffer from a lack of popularity in practice, mainly due to their high computational cost and absence of software implementation. We propose a novel formal approach to prior sensitivity analysis, which is fast and accurate. It quantifies sensitivity without the need for a model re-fit. Through a series of examples we show how our approach can be used to detect high prior sensitivities of some parameters as well as identifiability issues in possibly over-parametrized Bayesian hierarchical models.

Original languageEnglish (US)
Pages (from-to)321-349
Number of pages29
JournalBayesian Analysis
Volume10
Issue number2
DOIs
StatePublished - Jan 1 2015

Keywords

  • Base prior
  • Bayesian hierarchical models
  • Bayesian robustness
  • Calibration
  • Formal local sensitivity measure
  • Hellinger distance
  • Identifiability
  • Overparametrisation

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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