Imprecise Probability and Chance

Probability, chance and the probability of chance

In our day-to-day discourse on uncertainty, words like belief, chance, plausible, likelihood and probability are commonly encountered. Often, these words are used interchangeably, because they are intended to encapsulate some loosely articulated notions about the unknowns. The purpose of this paper is to propose a framework that is able to show how each of these terms can be made precise, so th...

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 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...

Probability and Chance

The weather report says that the chance of a hurricane arriving later today is 90%. Forewarned is forearmed: expecting a hurricane, before leaving home you pack your hurricane lantern. Probability enters into this scenario twice, first in the form of a physical probability, sometimes called a chance, quantifying certain aspects of the local weather that make a hurricane very likely, and second ...