An intelligent agent uses known facts, including statistical knowledge, to assign degrees of belief to assertions it is uncertain about. We investigate three principled techniques for doing this. All three are applications of the principle of indifference, because they assign equal degree of belief to all basic "situations " consistent with the knowledge base. They differ because there are competing intuitions about what the basic situations are. Various natural patterns of reasoning, such as the preference for the most specific statistical data available, turn out to follow from some or all of the techniques. This is an improvement over earlier theories, such as work on direct inference and reference classes, which arbitrarily postulate these patterns without offering any deeper explanations or guarantees of consistency. The three methods we investigate have surprising characterizations: there are connections to the principle of maximum entropy, a principle of maximal independence, an...

Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization, to handle updates that involve uncertain information. In this paper we re-examine such a case: van Fraassen's Judy Benjamin problem [1987], which in essence asks how one might update given the value of a conditional probability. We argue that---contrary to the suggestions in the literature---it is possible to use simple conditionalization in this case, and thereby obtain answers that agree fully with intuition. This contrasts with proposals such as cross-entropy, which are easier to apply but can give unsatisfactory answers. Based on the lessons from this example, we speculate on some general philosophical issues concerning probability update. 1 INTRODUCTION How should one update one's beliefs, represented as a probability distribution Pr over some ...

In previous work [BGHK92, BGHK93], we have studied the random-worlds approach---a particular (and quite powerful) method for generating degrees of belief (i.e., subjective probabilities) from a knowledge base consisting of objective (first-order, statistical, and default) information. But allowing a knowledge base to contain only objective information is sometimes limiting. We occasionally wish to include information about degrees of belief in the knowledge base as well, because there are contexts in which old beliefs represent important information that should influence new beliefs. In this paper, we describe three quite general techniques for extending a method that generates degrees of belief from objective information to one that can make use of degrees of belief as well. All of our techniques are based on well-known approaches, such as cross-entropy. We discuss general connections between the techniques and in particular show that, although conceptually and techn...

This paper is an o shoot of a much larger project which started about 17 years ago with an attempt to construct an expert system for medical diagnosis. The idea, and such ideas were common at that time, and probably still are for all we know, was to program a computer so that it would be enough to type in the patient's signs, symptoms, personal details etc. and the computer would come up with a quali ed diagnosis, just in the way a doctor appears to do