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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.
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.
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