Subjective probability models for lifetimes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2001
|
| Schriftenreihe: | Monographs on statistics and applied probability
91 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 248 S. graph. Darst. |
| ISBN: | 1584880600 |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: Subjective probability models for lifetimes
Autor: Spizzichino, Fabio
Jahr: 2001
Contents Preface xiii Notation and Acronyms xvii 1 Exchangeability and subjective probability 1 1.1 Introduction.............................. 1 1.2 Families of exchangeable events................... 6 1.2.1 Extendibility and de Finetti’s theorem........... 12 1.2.2 The problem of prediction ................. 15 1.2.3 More on infinitely extendible families............ 18 1.3 Exchangeable random quantities.................. 21 1.3.1 Extendibility and de Finetti’s theorem for exchangeable random variables....................... 23 1.3.2 The problem of prediction.................. 29 1.4 de Finetti-type theorems and parametric models.........32 1.4.1 Parametric models and prediction sufficiency.......35 1.5 Exercises ............................... 39 1.6 Bibliography .............................42 2 Exchangeable lifetimes 47 2.1 Introduction.............................. 47 2.2 Positive exchangeable random quantities.............. 52 2.3 Multivariate conditional hazard rates................ 70 2.4 Further aspects of m.c.h.r........ 80 2.4.1 On the use of the m.c.h.r. functions............ 80 2.4.2 Dynamic histories, total time on test statistic and total hazard transform....................... 83 2.4.3 M.c.h.r. functions and dynamic sufficiency......... 90 2.5 Exercises ............................... 92 2.6 Bibliography ............................. 95 IX
X 3 Some concepts of dependence and aging 99 3.1 Introduction..............................99 3.1.1 One-dimensional stochastic orderings............101 3.1.2 Stochastic monotonicity and orderings for conditional distributions .........................105 3.2 Multivariate stochastic orderings..................107 3.2.1 Usual multivariate stochastic ordering...........107 3.2.2 Multivariate likelihood ratio ordering............109 3.2.3 Multivariate hazard rate and cumulative hazard rate orderings...........................110 3.2.4 Some properties of multivariate stochastic orderings and examples ...........................Ill 3.3 Some notions of dependence....................115 3.3.1 Positive dependence.....................115 3.3.2 Negative dependence.....................120 3.3.3 Simpson-type paradoxes and aspects of dependence in Bayesian analysis.......................122 3.3.4 Likelihood-ratio comparisons between posterior distributions .........................124 3.4 Some notions
of aging........................128 3.4.1 One-dimensional notions of aging.......... 128 3.4.2 Dynamic multivariate notions of aging...........134 3.4.3 The case of exchangeable lifetimes.............136 3.5 Exercises ...............................140 3.6 Bibliography .............................143 4 Bayesian models of aging 147 4.1 Introduction..............................147 4.2 Schur survival functions.......................151 4.2.1 Basic background about majorization...........152 4.2.2 Schur properties of survival functions and multivariate aging .............................156 4.2.3 Examples of Schur survival functions............160 4.2.4 Schur survival functions and dependence..........163 4.3 Schur density functions .......................164 4.3.1 Schur-constant densities...................166 4.3.2 Examples of Schur densities.................169 4.3.3 Properties of Schur densities ................172 4.4 Further aspects of Bayesian aging..................176 4.4.1 Schur
densities and TTT plots...............176 4.4.2 Some other notions of Bayesian aging...........179 4.4.3 Heterogeneity and multivariate negative aging.......180 4.4.4 A few bibliographical remarks................183
xi 4.4.5 Extensions to non-exchangeable cases...........183 4.5 Exercises ...............................184 4.6 Bibliography .............................187 5 Bayesian decisions, orderings, and majorization 191 5.1 Introduction..............................191 5.1.1 Statistical decision problems ................196 5.1.2 Statistical decision problems and sufficiency........203 5.1.3 Some technical aspects....................204 5.2 Stochastic orderings and orderings of decisions..........206 5.3 Orderings of residual lifetimes and majorization..........212 5.3.1 The case of observations containing failure data......218 5.4 Burn-in problems for exchangeable lifetimes............224 5.4.1 The case of i.i.d. lifetimes..................225 5.4.2 Dependence and optimal adaptive burn-in procedures . . 228 5.4.3 Burn-in, optimal stopping, monotonicity, and Markovianity.........................231 5.4.4 Stochastic orderings and open-loop optimal adaptive burn-in procedures......................233 5.5 Exercises . . ^ . . . .........................240 5.6 Bibliography .............................241 Essential bibliography 245 Index 247
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:58:09Z |
| institution | BVB |
| isbn | 1584880600 |
| language | English |
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| series | Monographs on statistics and applied probability |
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| spelling | Spizzichino, Fabio Verfasser aut Subjective probability models for lifetimes Fabio Spizzichino Boca Raton [u.a.] Chapman & Hall/CRC 2001 XX, 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 91 Methode van Bayes gtt Waarschijnlijkheidstheorie gtt Failure time data analysis Probabilities Subjektive Wahrscheinlichkeit (DE-588)4133277-5 gnd rswk-swf Subjektive Wahrscheinlichkeit (DE-588)4133277-5 s DE-604 Monographs on statistics and applied probability 91 (DE-604)BV002494005 91 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009681291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spizzichino, Fabio Subjective probability models for lifetimes Monographs on statistics and applied probability Methode van Bayes gtt Waarschijnlijkheidstheorie gtt Failure time data analysis Probabilities Subjektive Wahrscheinlichkeit (DE-588)4133277-5 gnd |
| subject_GND | (DE-588)4133277-5 |
| title | Subjective probability models for lifetimes |
| title_auth | Subjective probability models for lifetimes |
| title_exact_search | Subjective probability models for lifetimes |
| title_full | Subjective probability models for lifetimes Fabio Spizzichino |
| title_fullStr | Subjective probability models for lifetimes Fabio Spizzichino |
| title_full_unstemmed | Subjective probability models for lifetimes Fabio Spizzichino |
| title_short | Subjective probability models for lifetimes |
| title_sort | subjective probability models for lifetimes |
| topic | Methode van Bayes gtt Waarschijnlijkheidstheorie gtt Failure time data analysis Probabilities Subjektive Wahrscheinlichkeit (DE-588)4133277-5 gnd |
| topic_facet | Methode van Bayes Waarschijnlijkheidstheorie Failure time data analysis Probabilities Subjektive Wahrscheinlichkeit |
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