Subjective Probability Models for Lifetimes
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Summary
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.
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
References
Editorial Reviews
"…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 Mathematik
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