Indifference, Independence and MaxEnt

Manfred Schramm and Michael Greiner

Abstract

Through completing an underspecified probability model, ME supports non-monotonic inferences. Some major aspects of how this is done by ME can be understood from the background of two principles of rational decision: the concept of indifference and the concept of independence. In a formal specification ME can be viewed as (conservative) extension of these principles; so these principles shed light on the ``magical'' decisions of ME. But the other direction is true as well: Since ME is a ``correct'' representation of the set of models (Concentration-Theorem), it elucidates these two principles (e.g. it can be shown, that the knowledge of independencies can be of very different information-theoretic value). These principles and their calculi are not just arbitrary ideas: When extended to work with qualitative constraints which are modelled by probability intervals, each calculus can be successfully applied to V. Lifschitz`s Benchmarks and is able to infer some instances of them. Since ME is strictly stronger than the combination of the two principles, it yields a powerful tool for decisions in situations of incomplete knowledge. To give an example, a well-known problem of statistical inference (Simpson-Paradox) will serve as an illustration throughout the talk.
MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk