## Bayesian Analysis

### Optimal Robustness Results for Relative Belief Inferences and the Relationship to Prior-Data Conflict

#### Abstract

The robustness to the prior of Bayesian inference procedures based on a measure of statistical evidence is considered. These inferences are shown to have optimal properties with respect to robustness. Furthermore, a connection between robustness and prior-data conflict is established. In particular, the inferences are shown to be effectively robust when the choice of prior does not lead to prior-data conflict. When there is prior-data conflict, however, robustness may fail to hold.

#### Article information

Source
Bayesian Anal., Volume 12, Number 3 (2017), 705-728.

Dates
First available in Project Euclid: 7 September 2016

https://projecteuclid.org/euclid.ba/1473276256

Digital Object Identifier
doi:10.1214/16-BA1024

Mathematical Reviews number (MathSciNet)
MR3655873

Zentralblatt MATH identifier
1384.62076

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62F35: Robustness and adaptive procedures

#### Citation

Al Labadi, Luai; Evans, Michael. Optimal Robustness Results for Relative Belief Inferences and the Relationship to Prior-Data Conflict. Bayesian Anal. 12 (2017), no. 3, 705--728. doi:10.1214/16-BA1024. https://projecteuclid.org/euclid.ba/1473276256

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