Logics of imprecise comparative probability

Imprecise probability trees: Bridging two theories of imprecise probability

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley’s behavioural theory of imprecise probabilities, and Shafer and Vovk’s game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that...

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...

Constructing imprecise probability distributions

In this current paper the following problems are addressed: (1) extending the knowledge of a partially known probability distribution function to any point of a continuous sample space, (2) constructing an imprecise probability distribution based on the knowledge of a set of credible or confidence intervals, and (3) computing the lower and upper expected values of a random continuous variable. ...

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...