Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

The approach to probability theory followed in this book characterizes probability as a linear operator rather than as a measure, and is based on the concept of coherence, which can be framed in the most general view of conditional probability. It is a `flexible' and unifying tool suited for handling, e.g., partial probability assessments, and conditional independence, in a way that avoids all the inconsistencies related to logical dependence. Moreover, it is possible to encompass other approaches to uncertain reasoning, such (...) as fuzziness, possibility functions, and default reasoning. The book is kept self-contained, provided the reader is familiar with the elementary aspects of propositional calculus, linear algebra, and analysis. (shrink)

Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which (...) amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. (shrink)