Imprecise Probabilities in Statistics and Philosophy

Breadcrumb Navigation


Keynote Speakers

Fabio Cozman (Professor at the Engineering School of the University of São Paulo, Brazil). Professor Cozman earned his PhD. from Carnegie Mellon University. Besides imprecise probabilities, he has worked on robotics and probabilistic reasoning with graphical models. His research on inference and decision-making with imprecise probabilities has focussed in particular on credal networks, independence concepts, and sequential decision making. For more information, visit his website.


Graph-theoretical Models for Imprecise Probabilities: Independence Assumptions, Logical Constructs


Research in artificial intelligence systems has often employed graphs to encode multivariate probability distributions. Such graph-theoretical formalisms heavily employ independence assumptions so as to simplify model construction and manipulation. Another line of research has focused on the combination of logical and probabilistic formalisms for knowledge representation, often without any explicit discussion of independence assumptions. In this talk we examine (1) graph-theoretical models, called credal networks, that represent sets of probability distributions and various independence assumptions; and (2) languages that combine logical constructs with graph-theoretical models, so as to provide tractability and flexibility. The challenges in combining these various formalisms are discussed, together with insights on how to make them work together.

James M. Joyce (Professor of Philosophy and of Statistics, University of Michigan). Professor Joyce was awarded his PhD. by the University of Michigan in 1991. As well as imprecise probabilities, his research interests include rational choice theory, causal reasoning, Bayesian approaches to statistics and inductive inference. His book "Foundations of Causal Decision Theory" (1999, Cambridge University Press) is considered the standard reference on causal decision theory. For more information, visit his website.


Imprecise Priors as Expressions of Epistemic Value


As is well known, imprecise prior probabilities can help us model beliefs in contexts where evidence is sparse, equivocal or vague. It is less well-known that they can also provide a useful way of representing certain kinds of indecision or uncertainty about epistemic values and inductive policies. If we use the apparatus of proper scoring rules to model a believer's epistemic values, then we can see her 'choice' of a prior as, partly, an articulation of her values. In contexts where epistemic values and inductive policies are less than fully definite, or where there is unresolved conflict among values, the imprecise prior will reflect this indefiniteness in theoretically interesting ways.

Teddy Seidenfeld (Herbert A. Simon University Professor of Philosophy and Statistics, Carnegie Mellon University). Professor Seidenfeld earned his PhD. from Columbia in 1975. Professor Seidenfeld has worked on many aspects of imprecise probabilities including dilation, scoring rules for IP and coherent choice functions for IP. Other of his "foundational" research interests outside of IP theory (often pursued in collaborations with Jay Kadane and Mark Schervish) include finitely additive probability theory, the theory of conditional expectations, and coherent preferences for unbounded random variablesHe has also been influential on many other foundational topics at the intersection of statistics, decision theory and philosophy; these include: "state dependent" utilities, sequential decision making, reaching a consensus (judgement aggregation) and the value of information. For more information, visit his website.


Eliciting imprecise probabilities
(Based on joint work with Mark J. Schervish, and Joseph B. Kadane.)


I review de Finetti’s two coherence criteria for determinate probabilities:

  • coherence1, which is defined in terms of previsions (fair prices) for a set of random variables that are undominated by the status quo – previsions immune to a sure-loss –
  • and coherence2, which defined in terms of forecasts for random variables that are undominated in Brier score by a rival set of forecasts.

I review issues of elicitation associated with these two criteria that differentiate them, particularly when generalizing from eliciting determinate to eliciting imprecise probabilities.