On Resolving Problems with Conditionality and Its Implications for Characterizing Statistical Evidence

Michael Evans () and Constantine Frangakis ()
Additional contact information
Michael Evans: University of Toronto
Constantine Frangakis: Johns Hopkins University

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 2, No 1, 1103-1126

Abstract: Abstract The conditionality principle C plays a key role in attempts to characterize the concept of statistical evidence. The standard version of C considers a model and a derived conditional model, formed by conditioning on an ancillary statistic for the model, together with the data, to be equivalent with respect to their statistical evidence content. This equivalence is considered to hold for any ancillary statistic for the model but creates two problems. First, there can be more than one maximal ancillary in a given context and this leads to C not being an equivalence relation and, as such, calls into question whether C is a proper characterization of statistical evidence. Second, a statistic A can change from ancillary to informative (in its marginal distribution) when another ancillary B changes, from having one known distribution PB, to having another known distribution QB. This means that the stability of ancillarity differs across ancillary statistics and raises the issue of when a statistic can be said to be truly ancillary. It is therefore natural, and practically important, to limit conditioning to the set of ancillaries whose distribution is irrelevant to the ancillary status of any other ancillary statistic. This results in a family of ancillaries for which there is a unique maximal member. This also gives a new principle for inference, the stable conditionality principle, that satisfies the criteria required for any principle whose aim is to characterize statistical evidence.

Keywords: Ancillaries; stable ancillaries; strong ancillaries; the laminal ancillary; stable conditionality principle.; Primary: 62A01; Secondary: 62B99 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13171-022-00295-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00295-2

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-022-00295-2

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().