Subjective Probability Models for Lifetimes

Subjective Probability Models for Lifetimes

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Description

Bayesian methods in reliability cannot be fully utilized and understood without full comprehension of the essential differences that exist between frequentist probability and subjective probability. Switching from the frequentist to the subjective approach requires that some fundamental concepts be rethought and suitably redefined. Subjective Probability Models for Lifetimes details those differences and clarifies aspects of subjective probability that have a direct influence on modeling and drawing inference from failure and survival data. In particular, within a framework of Bayesian theory, the author considers the effects of different levels of information in the analysis of the phenomena of positive and negative aging. The author coherently reviews and compares the various definitions and results concerning stochastic ordering, statistical dependence, reliability, and decision theory. He offers a detailed but accessible mathematical treatment of different aspects of probability distributions for exchangeable vectors of lifetimes that imparts a clear understanding of what the "probabilistic description of aging" really is, and why it is important to analyzing survival and failure data.show more

Product details

  • Hardback | 272 pages
  • 158 x 238.3 x 19.8mm | 542.44g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 20 black & white illustrations
  • 1584880600
  • 9781584880608

Review quote

"there is also much clear and helpful explanation of concepts particularly useful for research students." -Short Book Reviews of the ISI, April 2002 "The author's lucid presentation of his material together with this very great number of applications from life sciences, make this an excellent buy..." -Biometrics "even hard-bitten mathematical probabilists may find new insights in this insistently realistic approach." -Zentralblatt fur Mathematikshow more

Table of contents

EXCHANGEABILITY AND SUBJECTIVE PROBABILITY Introduction Families of Exchangeable Events Exchangeable random quantities de Finetti's type theorems and parametric models Exercises References EXCHANGEABLE LIFETIMES Introduction Non-negative exchangeable random quantities Multivariate conditional hazard rates Further aspects of conditional hazard rates Exercises References SOME CONCEPTS OF DEPENDENCE AND AGING Introduction Multivariate Stochastic Orderings Some notions of dependence Some notions of aging Exercises References BAYESIAN PROPERTIES OF AGING Introduction Schur survival functions Schur density functions Further aspects of Bayesian Aging Exercises References BAYESIAN DECISIONS, ORDERINGS, AND MAJORIZATION Introduction Stochastic orderings and orderings of decisions Stochastic orderings of residual lifetimes and majorization Burn-in problems for exchangeable lifetimes Exercises Referencesshow more