Bayesian Analysis

Sensitivity Analysis for Bayesian Hierarchical Models

Małgorzata Roos, Thiago G. Martins, Leonhard Held, and Håvard Rue

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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.

Article information

Source
Bayesian Anal., Volume 10, Number 2 (2015), 321-349.

Dates
First available in Project Euclid: 2 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.ba/1422884977

Digital Object Identifier
doi:10.1214/14-BA909

Mathematical Reviews number (MathSciNet)
MR3420885

Zentralblatt MATH identifier
1335.62059

Keywords
Base prior formal local sensitivity measure Bayesian robustness calibration Hellinger distance Bayesian hierarchical models identifiability overparametrisation

Citation

Roos, Małgorzata; Martins, Thiago G.; Held, Leonhard; Rue, Håvard. Sensitivity Analysis for Bayesian Hierarchical Models. Bayesian Anal. 10 (2015), no. 2, 321--349. doi:10.1214/14-BA909. https://projecteuclid.org/euclid.ba/1422884977


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