17,688 research outputs found
Believing Probabilistic Contents: On the Expressive Power and Coherence of Sets of Sets of Probabilities
Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Mossâ account of probabilistic knowledge or her semantics for epistemic modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower
probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch
bookability iff they have consistent probabilistic beliefs
Sets of Priors Reflecting Prior-Data Conflict and Agreement
In Bayesian statistics, the choice of prior distribution is often debatable,
especially if prior knowledge is limited or data are scarce. In imprecise
probability, sets of priors are used to accurately model and reflect prior
knowledge. This has the advantage that prior-data conflict sensitivity can be
modelled: Ranges of posterior inferences should be larger when prior and data
are in conflict. We propose a new method for generating prior sets which, in
addition to prior-data conflict sensitivity, allows to reflect strong
prior-data agreement by decreased posterior imprecision.Comment: 12 pages, 6 figures, In: Paulo Joao Carvalho et al. (eds.), IPMU
2016: Proceedings of the 16th International Conference on Information
Processing and Management of Uncertainty in Knowledge-Based Systems,
Eindhoven, The Netherland
The CONEstrip algorithm
Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs
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