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## Munich Center for Mathematical Philosophy (MCMP)

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Workshop on Imprecise Probabilities in Statistics and Philosophy, Teddy Seidenfeld (CMU) gives a talk at the Workshop on Imprecise Probabilities in Statistics and Philosophy (27-28 June, 2014) titled "Dominance and Elicitation in IP Theory". Abstract: I review de Finettis 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.

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Workshop on Imprecise Probabilities in Statistics and Philosophy, Fabio G. Cozman (Sao Paulo) gives a talk at the Workshop on Imprecise Probabilities in Statistics and Philosophy (27-28 June, 2014) titled "Imprecise (Full Conditional) Probabilities, Graphs and Graphoids Independence Assumptions". Abstract: 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 exibility. The challenges in combining these various formalisms are discussed, together with insights on how to make them work together.

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Workshop on Imprecise Probabilities in Statistics and Philosophy, Jim Joyce (Michigan) gives a talk at the Workshop on Imprecise Probabilities in Statistics and Philosophy (27-28 June, 2014) titled "Imprecise Priors as Expressions of Epistemic Values". Abstract: 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 reject this indefiniteness in theoretically interesting ways.

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