Bayesian ideas have recently been applied across such diverse fields as philosophy, statistics, economics, psychology, artificial intelligence, and legal theory. Fundamentals of Bayesian Epistemology examines epistemologists' use of Bayesian probability mathematics to represent degrees of belief. Michael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implications Volume 1 begins by motivating the use of degrees of belief in epistemology. It then introduces, explains, and applies the five core Bayesian normative rules: Kolmogorov's three probability axioms, the Ratio Formula for conditional degrees of belief, and Conditionalization for updating attitudes over time. Finally, it discusses further normative rules (such as the Principal Principle, or indifference principles) that have been proposed to supplement or replace the core five. Volume 2 gives arguments for the five core rules introduced in Volume 1, then considers challenges to Bayesian epistemology. It begins by detailing Bayesianism's successful applications to confirmation and decision theory. Then it describes three types of arguments for Bayesian rules, based on representation theorems, Dutch Books, and accuracy measures. Finally, it takes on objections to the Bayesian approach and alternative formalisms, including the statistical approaches of frequentism and likelihoodism.

Bayesian ideas have recently been applied across such diverse fields as philosophy, statistics, economics, psychology, artificial intelligence, and legal theory. Fundamentals of Bayesian Epistemology examines epistemologists' use of Bayesian probability mathematics to represent degrees of belief. Michael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implications Volume 1 begins by motivating the use of degrees of belief in epistemology. It then introduces, explains, and applies the five core Bayesian normative rules: Kolmogorov's three probability axioms, the Ratio Formula for conditional degrees of belief, and Conditionalization for updating attitudes over time. Finally, it discusses further normative rules (such as the Principal Principle, or indifference principles) that have been proposed to supplement or replace the core five. Volume 2 gives arguments for the five core rules introduced in Volume 1, then considers challenges to Bayesian epistemology. It begins by detailing Bayesianism's successful applications to confirmation and decision theory. Then it describes three types of arguments for Bayesian rules, based on representation theorems, Dutch Books, and accuracy measures. Finally, it takes on objections to the Bayesian approach and alternative formalisms, including the statistical approaches of frequentism and likelihoodism.

Michael G. Titelbaum presents a new Bayesian framework for modeling rational degrees of belief, called the Certainty-Loss Framework. Subjective Bayesianism is epistemologists' standard theory of how individuals should change their degrees of belief over time. But despite the theory's power, it is widely recognized to fail for situations agents face every day-cases in which agents forget information, or in which they assign degrees of belief to self-locating claims. Quitting Certainties argues that these failures stem from a common source: the inability of Conditionalization (Bayesianism's traditional updating rule) to model claims' going from certainty at an earlier time to less-than-certainty later on. It then presents a new Bayesian updating framework that accurately represents rational requirements on agents who undergo certainty loss. Titelbaum develops this new framework from the ground up, assuming little technical background on the part of his reader. He interprets Bayesian theories as formal models of rational requirements, leading him to discuss both the elements that go into a formal model and the general principles that link formal systems to norms. By reinterpreting Bayesian methodology and altering the theory's updating rules, Titelbaum is able to respond to a host of challenges to Bayesianism both old and new. These responses lead in turn to deeper questions about commitment, consistency, and the nature of information. Quitting Certainties presents the first systematic, comprehensive Bayesian framework unifying the treatment of memory loss and context-sensitivity. It develops this framework, motivates it, compares it to alternatives, then applies it to cases in epistemology, decision theory, the theory of identity, and the philosophy of quantum mechanics.