Bayesian influence diagnostics using normalized functional Bregman divergence

Ian M. Danilevicz and Ricardo S. Ehlers

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 6, 1637-1652

Abstract: Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods. Kullback-Leiber and Bregman divergences were already applied in Bayesian inference to measure the isolated impact of each observation in a model. We extend these ideas to models for dependent and independent data with normal and non-normal probability distributions. We also propose a strategy to rescale the functional Bregman divergence to lie in the (0,1) interval thus facilitating interpretation and comparison. This is accomplished with a minimal computational effort while maintaining all theoretical properties. For computational efficiency, we take advantage of Hamiltonian Monte Carlo methods to draw samples from the posterior distribution of model parameters. The resulting Markov chains are then directly connected with Bregman calculus, which results in fast computation. We check our proposed strategies in both simulated and empirical studies.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2020.1764583 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:51:y:2022:i:6:p:1637-1652

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2020.1764583

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().