Fundamentals of Bayesian epistemology / Michael G. Titelbaum.

Format:

Book

Author/Creator:

Titelbaum, Michael G., author.

Contributor:

Edward Potts Cheyney Memorial Fund.

Language:

English

Subjects (All):

Knowledge, Theory of.

Probabilities.

Probability.

epistemology.

probability.

Bayesian statistical decision theory.

Medical Subjects:

Probability.

Physical Description:

<1-2 > volumes : illustrations ; 24 cm

Edition:

First edition.

Place of Publication:

New York, NY : Oxford University Press, 2022-

Summary:

"This book introduces readers to the fundamentals of Bayesian epistemology. It begins by motivating and explaining the idea of a degree of belief (also known as a "credence"). It then presents Bayesians' five core normative rules governing degrees of belief: Kolmogorov's three probability axioms, the Ratio Formula for conditional credences, and Conditionalization for updating credences over time. After considering a few proposed additions to these norms, it applies the core rules to confirmation and decision theory. The book then details arguments for the Bayesian rules based on representation theorems, Dutch Books, and accuracy measures. Finally, it looks at objections and challenges to Bayesian epistemology. It presents problems concerning memory loss, self-location, old evidence, logical omniscience, and the subjectivity of priors. It considers the rival statistical paradigms of frequentism and likelihoodism. Then it explores alternative Bayesian-style formalisms involving comparative confidence rankings, credences ranges, and Dempster-Shafer functions"-- Provided by publisher.

Contents:

Machine generated contents note: VOLUME 1

I. OUR SUBJECT

1. Beliefs and Degrees of Belief

1.1. Binary beliefs

1.1.1. Classificatory, comparative, quantitative

1.1.2. Shortcomings of binary belief

1.2. From binary to graded

1.2.1. Comparative confidence

1.2.2. Bayesian epistemology

1.2.3. Relating beliefs and credences

1.3. The rest of this book

1.4. Exercises

1.5. Further reading

II. THE BAYESIAN FORMALISM

2. Probability Distributions

2.1. Propositions and propositional logic

2.1.1. Relations among propositions

2.1.2. State-descriptions

2.1.3. Predicate logic

2.2. The probability axioms

2.2.1. Consequences of the probability axioms

2.2.2. A Bayesian approach to the Lottery scenario

2.2.3. Doxastic possibilities

2.2.4. Probabilities are weird! The Conjunction Fallacy

2.3. Alternative representations of probability

2.3.1. Probabilities in Venn diagrams

2.3.2. Probability tables

2.3.3. Using probability tables

2.3.4. Odds

2.4. What the probability calculus adds

2.5. Exercises

2.6. Further reading

3. Conditional Credences

3.1. Conditional credences and the Ratio Formula

3.1.1. The Ratio Formula

3.1.2. Consequences of the Ratio Formula

3.1.3. Bayes's Theorem

3.2. Relevance and independence

3.2.1. Conditional independence and screening off

3.2.2. The Gambler's Fallacy

3.2.3. Probabilities are weird! Simpson's Paradox

3.2.4. Correlation and causation

3.3. Conditional credences and conditionals

3.4. Exercises

3.5. Further reading

4. Updating by Conditionalization

4.1. Conditionalization

4.1.1. Consequences of Conditionalization

4.1.2. Probabilities are weird! The Base Rate Fallacy

4.2. Evidence and certainty

4.2.1. Probabilities are weird! Total Evidence and the Monty Hall Problem

4.3. Priors and standards

4.3.1. Initial priors

4.3.2. Epistemic standards

4.3.3. Hypothetical priors

4.4. Exercises

4.5. Further reading

5. Further Rational Constraints

5.1. Subjective and Objective Bayesianism

5.1.1. Frequencies and propensities

5.1.2. Two distinctions in Bayesianism

5.2. Deference principles

5.2.1. The Principal Principle

5.2.2. Expert principles and Reflection

5.3. The Principle of Indifference

5.4. Credences for infinitely many possibilities

5.5. Jeffrey Conditionalization

5.6. Exercises

5.7. Further reading

VOLUME 2

III. APPLICATIONS

6. Confirmation

6.1. Formal features of the confirmation relation

6.1.1. Confirmation is weird! The Paradox of the Ravens

6.1.2. Further adequacy conditions

6.2. Carnap's theory of confirmation

6.2.1. Confirmation as relevance

6.2.2. Finding the right function

6.3. Grue

6.4. Subjective Bayesian confirmation

6.4.1. Confirmation measures

6.4.2. Subjective Bayesian solutions to the Paradox of the Ravens

6.5. Exercises

6.6. Further reading

7. Decision Theory

7.1. Calculating expectations

7.1.1. The move to utility

7.2. Expected utility theory

7.2.1. Preference rankings and money pumps

7.2.2. Savage's expected utility

7.2.3. Jeffrey's theory

7.2.4. Risk aversion and Allais' Paradox

7.3. Causal Decision Theory

7.3.1. Newcomb's Problem

7.3.2. A causal approach

7.3.3. Responses and extensions

7.4. Exercises

7.5. Further reading

IV. ARGUMENTS FOR BAYESIANISM

8. Representation Theorems

8.1. Ramsey's four-step process

8.2. Savage's representation theorem

8.3. Representation theorems and probabilism

8.3.1. Objections to the argument

8.3.2. Reformulating the argument

8.4. Exercises

8.5. Further reading

9. Dutch Book Arguments

9.1. Dutch Books

9.1.1. Dutch Books for probabilism

9.1.2. Further Dutch Books

9.2. The Dutch Book Argument

9.2.1. Dutch Books depragmatized

9.3. Objections to Dutch Book Arguments

9.3.1. The Package Principle

9.3.2. Dutch Strategy objections

9.4. Exercises

9.5. Further reading

10. Accuracy Arguments

10.1. Accuracy as calibration

10.2. The gradational accuracy argument for probabilism

10.2.1. The Brier score

10.2.2. Joyce's accuracy argument for probabilism

10.3. Objections to the accuracy argument for probabilism

10.3.1. The absolute-value score

10.3.2. Proper scoring rules

10.3.3. Are improper rules unacceptable?

10.4. Do we really need Finite Additivity?

10.5. An accuracy argument for Conditionalization

10.6. Exercises

10.7. Further reading

V. CHALLENGES AND OBJECTIONS

11. Memory Loss and Self-locating Credences

11.1. Memory loss

11.1.1. The problem

11.1.2. A possible solution

11.1.3. Suppositional Consistency

11.2. Self-locating credences

11.2.1. The problem

11.2.2. The HTM approach

11.2.3. Going forward

11.3. Exercises

11.4. Further reading

12. Old Evidence and Logical Omniscience

12.1. Old evidence

12.1.1. The problem

12.1.2. Solutions to the diachronic problem

12.1.3. Solutions to the synchronic problem

12.1.4. More radical solutions

12.2. Logical omniscience

12.2.1. Clutter avoidance and partial distributions

12.2.2. Logical confirmation and logical learning

12.2.3. Allowing logical uncertainty

12.2.4. Logical omniscience reconsidered

12.3. Exercises

12.4. Further reading

13. The Problem of the Priors and Alternatives to Bayesianism

13.1. The Problem of the Priors

13.1.1. Understanding the problem

13.1.2. Washing out of priors

13.2. Frequentism

13.2.1. Significance testing

13.2.2. Troubles with significance testing

13.3. Likelihoodism

13.3.1. Troubles with likelihoodism

13.4. Exercises

13.5. Further reading

14. Comparative Confidence, Ranged Credences, and Dempster-Shafer Theory

14.1. Comparative confidence

14.1.1. De Finetti's comparative conditions

14.1.2. The Scott Axiom

14.1.3. Extensions and challenges

14.2. Ranged credences

14.2.1. Ranged credences, representation, and evidence

14.2.2. Extensions and challenges

14.3. Dempster-Shafer theory

14.4. Exercises

14.5. Further reading.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Edward Potts Cheyney Memorial Fund.

ISBN:

9780198707608

0198707606

9780198707615

0198707614

9780192863140

0192863142

9780192863157

0192863150

OCLC:

1291363790

Publisher Number:

99991891174