## The Annals of Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 62A15

Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

**Keywords**

Subjective probability systems Bayes rule measurable utility elicitation of subjective probabilities statistical decision theory

#### Citation

Manski, Charles F. Learning and Decision Making when Subjective Probabilities have Subjective Domains. Ann. Statist. 9 (1981), no. 1, 59--65. doi:10.1214/aos/1176345332. https://projecteuclid.org/euclid.aos/1176345332