A Study on the Power Parameter in Power Prior Bayesian Analysis

Zifei Han, Keying Ye and Min Wang

The American Statistician, 2023, vol. 77, issue 1, 12-19

Abstract: The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a fractional power δ. The derivation of the marginal likelihood based on the original power prior, and its variation, the normalized power prior, introduces a scaling factor C(δ) in the form of a prior predictive distribution with powered likelihood. In this article, we show that the scaling factor might be infinite for some positive δ with conventionally used initial priors, which would change the admissible set of the power parameter. This result seems to have been almost completely ignored in the literature. We then illustrate that such a phenomenon may jeopardize the posterior inference under the power priors when the initial prior of the model parameters is improper. The main findings of this article suggest that special attention should be paid when the suggested level of borrowing is close to 0, while the actual optimum might be below the suggested value. We use a normal linear model as an example for illustrative purposes.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/00031305.2022.2046160 (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:amstat:v:77:y:2023:i:1:p:12-19

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UTAS20

DOI: 10.1080/00031305.2022.2046160

Access Statistics for this article

The American Statistician is currently edited by Eric Sampson

More articles in The American Statistician from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().