# 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