# Chapter 2. The Quantification of Uncertainty

Published Online: 19 NOV 2007

DOI: 10.1002/9780470060346.ch2

Copyright © 2006 John Wiley & Sons, Ltd

Book Title

## Reliability and Risk: A Bayesian Perspective

Additional Information

#### How to Cite

Singpurwalla, N. D. (2006) The Quantification of Uncertainty, in Reliability and Risk: A Bayesian Perspective, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470060346.ch2

#### Publication History

- Published Online: 19 NOV 2007
- Published Print: 4 AUG 2006

#### Book Series:

#### Book Series Editors:

- Walter A. Shewhart and
- Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780470855027

Online ISBN: 9780470060346

- Summary
- Chapter

### Keywords:

- quantification of uncertainty;
- probability and quantification of uncertainty;
- finite additivity property of probability;
- subjective probabilities;
- law of total probability and Bayes' law;
- Bayesian paradigm for statistical inference and noncompetitive decision making;
- probability models, parameters, inference and prediction;
- testing hypotheses - posterior odds and Bayes factors;
- decision trees and influence diagrams for risk analysis

### Summary

This chapter contains sections titled:

Uncertain Quantities and Uncertain Events: Their Definition and Codification

Probability: A Satisfactory Way to Quantify Uncertainty

Overview of the Different Interpretations of Probability

Extending the Rules of Probability: Law of Total Probability and Bayes' Law

The Bayesian Paradigm: A Prescription for Reliability, Risk and Survival Analysis

Probability Models, Parameters, Inference and Prediction

Testing Hypotheses: Posterior Odds and Bayes Factors

Utility as Probability and Maximization of Expected Utility

Decision Trees and Influence Diagrams for Risk Analysis