THE DEVELOPMENT OF SUBJECTIVE BAYESIANISM

The Bayesian approach to inductive reasoning originated in two brilliant in-sights. In 1654 Blaise Pascal, while in the course of a correspondence with Fermat [1769], recognized that states of uncertainty can be quantified using probabili-ties and expectations. In the early 1760s Thomas Bayes [1763] first understood that learning can be represented probabilistically using what is now called Bayes’s Theorem. These ideas serve as the basis for all Bayesian thought. 1.1 Pascal’s Insights: Probability and Expectation In modern terms, Pascal’s insight is that uncertainty about the occurrence of an event can be expressed as a probability and, more generally, that uncertainty about the value of a quantity can be expressed as a mathematical expectation. The basic objects of uncertainty can be thought as propositions or events in a non-empty Boolean algebra Ω that is closed under negation and countable disjunction. A probability function on Ω is a mapping P of Ω into real numbers that obeys these laws