## The Annals of Statistics

### Predictive Likelihood

David Hinkley

#### 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

http://projecteuclid.org/euclid.aos/1176344723

JSTOR

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]

#### 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.