Paul Snow

AIJ Journal 1999 Journal Article

Diverse confidence levels in a probabilistic semantics for conditional logics

• Paul Snow

It has long been known that several popular default and conditional logics exactly describe infinitesimal probability constructs which betoken virtual certainty regarding the truth of one sentence if some other sentence is true. That the rules for default inference also describe a scheme of approximate inference for all positive-valued conditional probabilities has also long been known. More recently, a class of standard probability measures has been found whose expression of more likely than not is exactly described by default rules. This class can be extended by straightforward algebra so that the range of confidence levels expressed by standard probability distributions which are exactly described by the rules is as complete as for the approximate methods.

AIJ Journal 1998 Journal Article

The vulnerability of the transferable belief model to Dutch books

• Paul Snow

Smets and Kennes have claimed that the transferable belief model, a decision and inference procedure based upon the Dempster-Shafer formalism, never exposes the believer to a kind of betting conundrum known as a “Dutch book”. A Dutch book is constructed against the model in an elaboration of an example proposed by Smets and Kennes. A condition which permits this Dutch book is identified, and is shown to conflict with an intuition about reasonable belief revision which is not confined to the probabilist community.

UAI Conference 1994 Conference Paper

Ignorance and the Expressiveness of Single- and Set-Valued Probability Models of Belief

• Paul Snow

AAAI Conference 1994 Conference Paper

The Emergence of Ordered Belief from Initial Ignorance

• Paul Snow

Some simple assumptions about prior ignorance, and the idea that a sticiently arresting contrast in the likelihoods of evidence will elicit belief that one proposition is at least as belief-worthy as another, lead to a partial ordering of propositions without the use of any hind of prior probability. The partial ordering is mt a posterior probability distribution, but does share some intuitively pleasing properties of a probability, such as complementarity. Deciding the order (if any) between two disjunctions depends only on the highest likelihood disjunct in each, and so query handling in partitioned domains is efficient. In the event that an ordinary probability distribution is required for coherent decision making one can be quickly calculated from the partial order.

UAI Conference 1992 Conference Paper

Intuitions about Ordered Beliefs Leading to Probabilistic Models

• Paul Snow

UAI Conference 1991 Conference Paper

Compressed Constraints in Probabilistic Logic and Their Revision

• Paul Snow

AAAI Conference 1986 Conference Paper

Bayesian Inference without Point Estimates

• Paul Snow

It is conventional to apply Bayes’ formula only to point estimates of the prior probabilities. This convention is unnecessarily restrictive. The analyst may prefer to estimate that the priors belong to some set of probability vectors. Set estimates allow the non-paradoxical expression of ignorance and support rigorous inference on such everyday assertions as "one event is more likely than another" or that an event "usually" occurs. Bayes’ formula can revise set estimates, often at little computational cost beyond that needed for point priors. Set estimates can also inform statistical decisions, although disagreement exists about what decision methods are best.