- The Oxford Handbook of Probability and Philosophy
- List of Contributors
- Introduction
- Probability for Everyone—Even Philosophers
- Pre-history of Probability
- Probability in 17th- and 18th-century Continental Europe from the Perspective of Jacob Bernoulli’s <i>Art of Conjecturing</i>
- Probability and Its Application in Britain during the 17th and 18th Centuries
- A Brief History of Probability Theory from 1810 to 1940
- The Origins of Modern Statistics: The English Statistical School
- The Origins of Probabilistic Epistemology: Some Leading 20th-century Philosophers of Probability
- Kolmogorov’s Axiomatization and Its Discontents
- Conditional Probability
- The Bayesian Network Story
- Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision
- Probability and Nonclassical Logic
- A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions
- Imprecise and Indeterminate Probabilities
- Symmetry Arguments in Probability
- Frequentism
- Subjectivism
- Bayesianism vs. Frequentism in Statistical Inference
- The Propensity Interpretation
- Best System Approaches to Chance
- Probability and Randomness
- Chance and Determinism
- Human Understandings of Probability
- Probability Elicitation
- Probabilistic Opinion Pooling
- Quantum Probability: An Introduction
- Probabilities in Statistical Mechanics
- Probability in Biology: The Case of Fitness
- Probability in Epistemology
- Confirmation Theory
- Self-Locating Credences
- Probability in Logic
- Probability in Ethics
- Probability and the Philosophy of Religion
- Probability in Philosophy of Language
- Decision Theory
- Probabilistic Causation
- Name Index
- Subject Index

## Abstract and Keywords

This chapter offers a discussion of imprecision and indeterminacy in probability values; that is, there is a focus on situations where one does not attach a single real number to every possible event. There are several theories and mathematical models regarding such imprecise and indeterminate probabilities. Among these are, for instance, lower/upper or interval probabilities or expectations, Choquet capacities, belief functions and credal sets. The chapter reviews the history of some of these models and theories, and then summarizes their main technical assumptions. Some subtleties concerning conditioning and independence are also reviewed. The chapter concludes with a brief discussion of modeling and of criteria for decision-making (minimality, maximality, E-admissibility).

Keywords: imprecise probability value, indeterminate probability value, sensitivity analysis, robustness analysis, probability interval, lower probability, lower prevision, credal set, Choquet capacity, belief function

Fabio Cozman, Engineering School, University of Sao Paolo

Access to the complete content on Oxford Handbooks Online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can''t find the answer there, please contact us.

- The Oxford Handbook of Probability and Philosophy
- List of Contributors
- Introduction
- Probability for Everyone—Even Philosophers
- Pre-history of Probability
- Probability in 17th- and 18th-century Continental Europe from the Perspective of Jacob Bernoulli’s <i>Art of Conjecturing</i>
- Probability and Its Application in Britain during the 17th and 18th Centuries
- A Brief History of Probability Theory from 1810 to 1940
- The Origins of Modern Statistics: The English Statistical School
- The Origins of Probabilistic Epistemology: Some Leading 20th-century Philosophers of Probability
- Kolmogorov’s Axiomatization and Its Discontents
- Conditional Probability
- The Bayesian Network Story
- Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision
- Probability and Nonclassical Logic
- A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions
- Imprecise and Indeterminate Probabilities
- Symmetry Arguments in Probability
- Frequentism
- Subjectivism
- Bayesianism vs. Frequentism in Statistical Inference
- The Propensity Interpretation
- Best System Approaches to Chance
- Probability and Randomness
- Chance and Determinism
- Human Understandings of Probability
- Probability Elicitation
- Probabilistic Opinion Pooling
- Quantum Probability: An Introduction
- Probabilities in Statistical Mechanics
- Probability in Biology: The Case of Fitness
- Probability in Epistemology
- Confirmation Theory
- Self-Locating Credences
- Probability in Logic
- Probability in Ethics
- Probability and the Philosophy of Religion
- Probability in Philosophy of Language
- Decision Theory
- Probabilistic Causation
- Name Index
- Subject Index