Foundations of Probability With Applications Selected Papers 1974–1995

Unlock the power of data with our comprehensive course on probability and statistics for effective data analysis!

In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory.

Presenting probability in a natural way, this book uses interesting, carefully selected instructive examples that explain the theory, definitions, theorems, and methodology. Fundamentals of Probability has been adopted by the American Actuarial Society as one of its main references for the mathematical foundations of actuarial science.

Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period.