## The Annals of Statistics

### Learning and Decision Making when Subjective Probabilities have Subjective Domains

Charles F. Manski

#### Abstract

This paper relaxes the conventional subjective probability setup by allowing the $\sigma$-algebra on which probabilities are defined to be subjective along with the probability measure. First, the role of the probability domain in existing statistical decision theory is examined. Then the existing theory is extended by characterizing the individual's selection of a probability domain as the outcome of a decision process.

#### Article information

Source
Ann. Statist., Volume 9, Number 1 (1981), 59-65.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345332

Digital Object Identifier
doi:10.1214/aos/1176345332

Mathematical Reviews number (MathSciNet)
MR600532

Zentralblatt MATH identifier
0451.62004

JSTOR