From Statistics to Beliefs

An intelligent agent uses known facts including statistical knowledge to assign degrees of belief to assertions it is un certain about We investigate three principled techniques for doing this All three are applications of the principle of indi erence because they assign equal degree of belief to all basic situations consistent with the knowledge base They di er because there are competing intuitions about what the basic situations are Various natural patterns of reasoning such as the preference for the most speci c sta tistical data available turn out to follow from some or all of the techniques This is an improvement over earlier the ories such as work on direct inference and reference classes which arbitrarily postulate these patterns without o ering any deeper explanations or guarantees of consistency The three methods we investigate have surprising charac terizations there are connections to the principle of maxi mum entropy a principle of maximal independence and a center of mass principle There are also unexpected con nections between the three that help us understand why the speci c language chosen for the knowledge base is much more critical in inductive reasoning of the sort we consider than it is in traditional deductive reasoning