The principles of uncertainty

494 Pages·2009·3.467 MB·English

by  Kalman, Maira

Statistical Theory and Methods
Texts in Statistical Science
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“[It is] a lovely book, one that I hope will be widely adopted as a course textbook.”
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—Michael Jordan, University of California, Berkeley
c Principles of
“A careful, complete, and lovingly written exposition of the subjective Bayesian
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viewpoint by one of its most eloquent and staunch defenders. Summarizes a p
lifetime of theory, methods, and application developments for the Bayesian l
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inferential engine. A must-read for anyone looking for a deep understanding
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of the foundations of Bayesian methods and what they offer modern statistical

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practice.”
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—Bradley P. Carlin, University of Minnesota

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An intuitive and mathematical introduction to subjective probability and
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Bayesian statistics.
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An accessible, comprehensive guide to the theory of Bayesian statistics, e
Principles of Uncertainty presents the subjective Bayesian approach, which has r
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played a pivotal role in game theory, economics, and the recent boom in Markov a
Chain Monte Carlo methods. Both rigorous and friendly, the book contains: i
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• Introductory chapters examining each new concept or assumption
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y
• Just-in-time mathematics – the presentation of ideas just before they are
applied
• Summary and exercises at the end of each chapter
• Discussion of maximization of expected utility
• The basics of Markov Chain Monte Carlo computing techniques
• Problems involving more than one decision-maker
Written in an appealing, inviting style, and packed with interesting examples,
Principles of Uncertainty introduces the most compelling parts of mathematics, K
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computing, and philosophy as they bear on statistics. Although many books d
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present the computation of a variety of statistics and algorithms while barely n
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skimming the philosophical ramifications of subjective probability, this book
takes a different tack. By addressing how to think about uncertainty, this book
gives readers the intuition and understanding required to choose a particular
method for a particular purpose.
Joseph B. Kadane
K12848
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Texts in Statistical Science
Principles of
Uncertainty
CHAPMAN & HALL/CRC
Texts in Statistical Science Series
Series Editors
Bradley P. Carlin, University of Minnesota, USA
Julian J. Faraway, University of Bath, UK
Martin Tanner, Northwestern University, USA
Jim Zidek, University of British Columbia, Canada
Analysis of Failure and Survival Data Elementary Applications of Probability Theory,
P. J. Smith Second Edition
H.C. Tuckwell
The Analysis of Time Series —
An Introduction, Sixth Edition Elements of Simulation
C. Chatfield B.J.T. Morgan
Applied Bayesian Forecasting and Time Series Epidemiology — Study Design and
Analysis Data Analysis, Second Edition
A. Pole, M. West and J. Harrison M. Woodward
Applied Nonparametric Statistical Methods, Essential Statistics, Fourth Edition
Fourth Edition D.A.G. Rees
P. Sprent and N.C. Smeeton
Exercises and Solutions in Biostatistical Theory
Applied Statistics — Handbook of GENSTAT L.L. Kupper, B.H. Neelon, and S.M. O’Brien
Analysis
Extending the Linear Model with R — Generalized
E.J. Snell and H. Simpson
Linear, Mixed Effects and Nonparametric Regression
Applied Statistics — Principles and Examples Models
D.R. Cox and E.J. Snell J.J. Faraway
Applied Stochastic Modelling, Second Edition A First Course in Linear Model Theory
N. Ravishanker and D.K. Dey
B.J.T. Morgan
Generalized Additive Models:
Bayesian Data Analysis, Second Edition
An Introduction with R
A. Gelman, J.B. Carlin, H.S. Stern
S. Wood
and D.B. Rubin
Graphics for Statistics and Data Analysis with R
Bayesian Ideas and Data Analysis: An Introduction
K.J. Keen
for Scientists and Statisticians
Interpreting Data — A First Course
R. Christensen, W. Johnson, A. Branscum,
in Statistics
and T.E. Hanson
A.J.B. Anderson
Bayesian Methods for Data Analysis,
Introduction to General and Generalized
Third Edition
Linear Models
B.P. Carlin and T.A. Louis
H. Madsen and P. Thyregod
Beyond ANOVA — Basics of Applied Statistics
An Introduction to Generalized
R.G. Miller, Jr. Linear Models, Third Edition
Computer-Aided Multivariate Analysis, A.J. Dobson and A.G. Barnett
Fourth Edition Introduction to Multivariate Analysis
A.A. Afifi and V.A. Clark C. Chatfield and A.J. Collins
A Course in Categorical Data Analysis Introduction to Optimization Methods and Their
T. Leonard Applications in Statistics
A Course in Large Sample Theory B.S. Everitt
T.S. Ferguson Introduction to Probability with R
Data Driven Statistical Methods K. Baclawski
P. Sprent Introduction to Randomized Controlled Clinical
Decision Analysis — A Bayesian Approach Trials, Second Edition
J.Q. Smith J.N.S. Matthews
Design and Analysis of Experiment with SAS Introduction to Statistical Inference and Its
J. Lawson Applications with R
M.W. Trosset
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Introduction to Statistical Limit Theory Randomization, Bootstrap and Monte Carlo
A.M. Polansky Methods in Biology, Third Edition
B.F.J. Manly
Introduction to Statistical Methods for
Clinical Trials
Readings in Decision Analysis
T.D. Cook and D.L. DeMets
S. French
Large Sample Methods in Statistics
Sampling Methodologies with Applications
P.K. Sen and J. da Motta Singer
P.S.R.S. Rao
Linear Models with R
Statistical Analysis of Reliability Data
J.J. Faraway
M.J. Crowder, A.C. Kimber,
Logistic Regression Models T.J. Sweeting, and R.L. Smith
J.M. Hilbe
Statistical Methods for Spatial Data Analysis
Markov Chain Monte Carlo — O. Schabenberger and C.A. Gotway
Stochastic Simulation for Bayesian Inference,
Statistical Methods for SPC and TQM
Second Edition
D. Bissell
D. Gamerman and H.F. Lopes
Statistical Methods in Agriculture and Experimental
Mathematical Statistics
Biology, Second Edition
K. Knight
R. Mead, R.N. Curnow, and A.M. Hasted
Modeling and Analysis of Stochastic Systems,
Statistical Process Control — Theory and Practice,
Second Edition
Third Edition
V.G. Kulkarni
G.B. Wetherill and D.W. Brown
Modelling Binary Data, Second Edition
Statistical Theory, Fourth Edition
D. Collett
B.W. Lindgren
Modelling Survival Data in Medical Research,
Statistics for Accountants
Second Edition
S. Letchford
D. Collett
Statistics for Epidemiology
Multivariate Analysis of Variance and Repeated
N.P. Jewell
Measures — A Practical Approach for Behavioural
Scientists Statistics for Technology — A Course in Applied
D.J. Hand and C.C. Taylor Statistics, Third Edition
C. Chatfield
Multivariate Statistics — A Practical Approach
B. Flury and H. Riedwyl Statistics in Engineering — A Practical Approach
A.V. Metcalfe
Pólya Urn Models
H. Mahmoud Statistics in Research and Development,
Second Edition
Practical Data Analysis for Designed Experiments
R. Caulcutt
B.S. Yandell
Stochastic Processes: An Introduction,
Practical Longitudinal Data Analysis
Second Edition
D.J. Hand and M. Crowder
P.W. Jones and P. Smith
Practical Statistics for Medical Research
D.G. Altman Survival Analysis Using S — Analysis of
Time-to-Event Data
A Primer on Linear Models
M. Tableman and J.S. Kim
J.F. Monahan
The Theory of Linear Models
Principles of Uncertainty
B. Jørgensen
J.B. Kadane
Time Series Analysis
Probability — Methods and Measurement
H. Madsen
A. O’Hagan
Time Series: Modeling, Computation, and Inference
Problem Solving — A Statistician’s Guide,
R. Prado and M. West
Second Edition
C. Chatfield
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Texts in Statistical Science
Principles of
Uncertainty
Joseph B. Kadane
Carnegie Mellon University
Pittsburgh, Pennsylvania, USA
K12848_FM.indd 5 4/6/11 3:22 PM
CRC Press
Taylor & Francis Group
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Dedication
To my teachers, my colleagues and my students. J. B. K.
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Contents
List of Figures xix
List of Tables xxi
Foreword xxiii
Preface xxv
1 Probability 1
1.1 Avoiding being a sure loser 1
1.1.1 Interpretation 5
1.1.2 Notes and other views 5
1.1.3 Summary 8
1.1.4 Exercises 8
1.2 Disjoint events 9
1.2.1 Summary 10
1.2.2 A supplement on induction 11
1.2.3 A supplement on indexed mathematical expressions 11
1.2.4 Intersections of events 12
1.2.5 Summary 12
1.2.6 Exercises 13
1.3 Events not necessarily disjoint 13
1.3.1 A supplement on proofs of set inclusion 14
1.3.2 Boole’s Inequality 15
1.3.3 Summary 16
1.3.4 Exercises 16
1.4 Random variables, also known as uncertain quantities 16
1.4.1 Summary 17
1.4.2 Exercises 17
1.5 Finite number of values 17
1.5.1 Summary 21
1.5.2 Exercises 21
1.6 Other properties of expectation 22
1.6.1 Summary 24
1.6.2 Exercises 25
1.7 Coherence implies not a sure loser 25
1.7.1 Summary 26
1.7.2 Exercises 26
1.8 Expectations and limits 26
1.8.1 A supplement on limits 26
1.8.2 Resuming the discussion of expectations and limits 27
1.8.3 Reference 28
ix