Foundations of Bayesianism

Foundations of Bayesianism is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today.
Some of these papers seek to clarify the relationships between Bayesian, causal and logical reasoning. Others consider the application of Bayesianism to artificial intelligence, decision theory, statistics and the philosophy of science and mathematics. The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach. The upshot is a plethora of new problems and directions for Bayesians to pursue.

The book will be of interest to graduate students or researchers who wish to learn more about Bayesianism than can be provided by introductory textbooks to the subject. Those involved with the applications of Bayesian reasoning will find essential discussion on the validity of Bayesianism and its limits, while philosophers and others interested in pure reasoning will find new ideas on normativity and the logic of belief.

Introduction: Bayesianism into the 21st Century.- Bayesianism, Causality and Networks.- Bayesianism and Causality, or, Why I am only a Half-Bayesian.- Causal Inference without Counterfactuals.- Foundations for Bayesian Networks.- Probabilistic Learning Models.- Logic, Mathematics and Bayesianism.- The Logic of Bayesian Probability.- Subjectivism, Objectivism and Objectivity in Bruno de Finetti’s Bayesianism.- Bayesianism in Mathematics.- Common Sense and Stochastic Independence.- Integrating Probabilistic and Logical Reasoning.- Bayesianism and Decision Theory.- Ramsey and the Measurement of Belief.- Bayesianism and Independence.- The Paradox of the Bayesian Experts.- Criticisms of Bayesianism.- Bayesian Learning and Expectations Formation: Anything Goes.- Bayesianism and the Fixity of the Theoretical Framework.- Principles of Inference and their Consequences.