The Annals of Statistics

Predictive Likelihood

David Hinkley

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Abstract

The likelihood function is the common basis of all parametric inference. However, with the exception of an ad hoc definition by Fisher, there has been no such unifying basis for prediction of future events, given past observations. This article proposes a definition of predictive likelihood which can help to remove some nonuniqueness problems in sampling-theory predictive inference, and which can produce a simple prediction analog of the Bayesian parametric result, posterior $\propto$ prior $\times$ likelihood, in many situations.

Article information

Source
Ann. Statist. Volume 7, Number 4 (1979), 718-728.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176344723

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176344723

Mathematical Reviews number (MathSciNet)
MR532237

Zentralblatt MATH identifier
0422.62003

Subjects
Primary: 62A10
Secondary: 62F25: Tolerance and confidence regions 62A15 60G25: Prediction theory [See also 62M20]

Keywords
Prediction confidence regions exponential families likelihood Bayesian methods statistical inference

Citation

Hinkley, David. Predictive Likelihood. The Annals of Statistics 7 (1979), no. 4, 718--728. doi:10.1214/aos/1176344723. http://projecteuclid.org/euclid.aos/1176344723.


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See also

    Corrections

    • See Correction: David V. Hinkley. Note: Correction to "Predictive Likelihood". Ann. Statist., Volume 8, Number 3 (1980), 694--694.