Subjective Probability Models for Lifetimes: 1st Edition (Hardback) book cover

Subjective Probability Models for Lifetimes

1st Edition

By Fabio Spizzichino

Chapman and Hall/CRC

272 pages | 20 B/W Illus.

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pub: 2001-06-28
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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.

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

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

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis