Data-based decisions under imprecise probability and least favorable models

Data-based decisions under imprecise probability and least favorable models

Data-based decision theory under imprecise probability has to deal with optimisation problems where direct solutions are often computationally intractable. Using the Γ-minimax optimality criterion, the computational effort may significantly be reduced in the presence of a least favorable model. In 1984, A. Buja derived a necessary and sufficient condition for the existence of a least favorable ...

Validation of imprecise probability models

Validation is the assessment of the match between a model’s predictions and any empirical observations relevant to those predictions. This comparison is straightforward when the data and predictions are deterministic, but is complicated when either or both are expressed in terms of uncertain numbers (i.e., intervals, probability distributions, p-boxes, or more general imprecise probability stru...

Imprecise probability models and their applications

This special issue of the International Journal of Approximate Reasoning (IJAR) grew out of the 5th International Symposium on Imprecise Probabilities and Their Applications (ISIPTA’07), held in the beautiful city of Prague, Czech Republic, in July 2007 (http://www.sipta.org/isipta07). The symposium was organized by Gert de Cooman, Jiřina Vejnarová, and Marco Zaffalon. The term imprecise probab...

Imprecise Probability

Imprecise Probability

1 Overview Quantification of uncertainty is mostly done by the use of precise probabilities: for each event A, a single (classical, precise) probability P (A) is used, typically satisfying Kolmogorov's axioms [4]. Whilst this has been very successful in many applications, it has long been recognized to have severe limitations. Classical probability requires a very high level of precision and co...