Noninformative priors and nuisance parameters

Bertrand S Clarke, Larry Wasserman

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We study the conflict between priors that are noninformative for a parameter of interest versus priors that are noninformative for the whole parameter. Our investigation leads us to maximize a functional that has two terms: an asymptotic approximation to a standardized expected Kullback-Leibler distance between the marginal prior and marginal posterior for a parameter of interest, and a penalty term measuring the distance of the prior from the Jeffreys prior. A positive constant multiplying the second terms determines the tradeoff between noninformativity for the parameter of interest and noninformativity for the entire parameter. As the constant increases, the prior tends to the Jeffreys prior. When the constant tends to 0, the prior becomes degenerate except in special cases. This prior does not have a closed-form solution, but we present a simple, numerical algorithm for finding the prior. We compare this prior to the Berger–Bernardo prior.

Original languageEnglish (US)
Pages (from-to)1427-1432
Number of pages6
JournalJournal of the American Statistical Association
Volume88
Issue number424
DOIs
StatePublished - Jan 1 1993

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Noninformative Prior
Nuisance Parameter
Jeffreys Prior
Term
Tend
Kullback-Leibler Distance
Asymptotic Approximation
Closed-form Solution
Numerical Algorithms
Penalty
Trade-offs
Maximise
Nuisance parameter
Entire

Keywords

  • Asymptotic information
  • Reference prior
  • Tradeoff prior

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Noninformative priors and nuisance parameters. / Clarke, Bertrand S; Wasserman, Larry.

In: Journal of the American Statistical Association, Vol. 88, No. 424, 01.01.1993, p. 1427-1432.

Research output: Contribution to journalArticle

Clarke, Bertrand S ; Wasserman, Larry. / Noninformative priors and nuisance parameters. In: Journal of the American Statistical Association. 1993 ; Vol. 88, No. 424. pp. 1427-1432.
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