**Fabio Cozman Lonnie Chrisman
e-mail: fgcozman@cs.cmu.edu, chrisman@lumina.com**

This work is a technical report at the School of Computer Science, Carnegie Mellon University (CMU-RI-TR 97-25).

Several theories of inference and decision employ sets of probability
distributions as the fundamental representation of (subjective)
belief. This paper investigates a frequentist connection between
empirical data and convex sets of probability distributions. Building
on earlier work by Walley and Fine, a framework is advanced in which
a sequence of random outcomes can be described as being drawn from
a convex *set* of distributions, rather than just from a single
distribution. The extra generality can be detected from observable
characteristics of the outcome sequence. The paper presents new
asymptotic convergence results paralleling the laws of large numbers
in probability theory, and concludes with a comparison between this
approach and approaches based on prior subjective constraints.

- Introduction
- Convex sets of distributions
- Interpretations of credal sets
- Estimating a credal set
- The estimation task
- Walley and Fine's estimation task
- The finite learning theorem for convex sets of distributions
- Comparison with subjective learning of convex sets of distributions
- Conclusion
- References

© Fabio Cozman[Send Mail?]

Sun Jun 29 22:16:40 EDT 1997