## The Annals of Statistics

### Bayes' Theorem for Choquet Capacities

#### Abstract

We give an upper bound for the posterior probability of a measurable set $A$ when the prior lies in a class of probability measures $\mathscr{P}$. The bound is a rational function of two Choquet integrals. If $\mathscr{P}$ is weakly compact and is closed with respect to majorization, then the bound is sharp if and only if the upper prior probability is 2-alternating. The result is used to compute bounds for several sets of priors used in robust Bayesian inference. The result may be regarded as a characterization of 2-alternating Choquet capacities.

#### Article information

Source
Ann. Statist., Volume 18, Number 3 (1990), 1328-1339.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347752

Digital Object Identifier
doi:10.1214/aos/1176347752

Mathematical Reviews number (MathSciNet)
MR1062711

Zentralblatt MATH identifier
0736.62026

JSTOR

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62F35: Robustness and adaptive procedures

#### Citation

Wasserman, Larry A.; Kadane, Joseph B. Bayes' Theorem for Choquet Capacities. Ann. Statist. 18 (1990), no. 3, 1328--1339. doi:10.1214/aos/1176347752. https://projecteuclid.org/euclid.aos/1176347752