Chapter 2. The Quantification of Uncertainty

  1. Nozer D. Singpurwalla

Published Online: 19 NOV 2007

DOI: 10.1002/9780470060346.ch2

Reliability and Risk: A Bayesian Perspective

Reliability and Risk: A Bayesian Perspective

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

Author Information

  1. The George Washington University, Washington DC, USA

Publication History

  1. Published Online: 19 NOV 2007
  2. Published Print: 4 AUG 2006

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470855027

Online ISBN: 9780470060346



  • 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


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