Imprecise probability trees: Bridging two theories of imprecise 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...

Imprecise Probability: Theories and Applications (ISIPTA'13)

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. ...