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E-raamat: Comparative Statistical Inference 3e 3rd Edition [Wiley Online]

(University of Nottingham, UK)
  • Wiley Online
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This fully updated and revised third edition, presents a wide ranging, balanced account of the fundamental issues across the full spectrum of inference and decision-making. Much has happened in this field since the second edition was published: for example, Bayesian inferential procedures have not only gained acceptance but are often the preferred methodology. This book will be welcomed by both the student and practising statistician wishing to study at a fairly elementary level, the basic conceptual and interpretative distinctions between the different approaches, how they interrelate, what assumptions they are based on, and the practical implications of such distinctions.

As in earlier editions, the material is set in a historical context to more powerfully illustrate the ideas and concepts.

* Includes fully updated and revised material from the successful second edition

* Recent changes in emphasis, principle and methodology are carefully explained and evaluated

* Discusses all recent major developments

* Particular attention is given to the nature and importance of basic concepts (probability, utility, likelihood etc)

* Includes extensive references and bibliography

Written by a well-known and respected author, the essence of this successful book remains unchanged providing the reader with a thorough explanation of the many approaches to inference and decision making.
Preface xi(4)
Preface to Second Edition xv(2)
Preface to Third Edition xvii(2)
Acknowledgements xix
Chapter
1. Introduction: Statistical Inference and Decision-making
1(28)
1.1 What is Statistics?
1(3)
1.2 Probability Models
4(3)
1.3 Relevant Information
7(6)
1.4 Statistical Inference and Decision-making
13(2)
1.5 Different Approaches
15(4)
1.6 Arbitrariness and Controversy
19(4)
1.7 Historical Comment and Further References
23(6)
Chapter
2. An Illustration of the Different Approaches
29(36)
2.1 A Practical Example
29(3)
2.2 Sample Data as the Sole Source of Information: the Classical Approach
32(15)
2.2.1 Batch Quality
33(10)
2.2.2 Component Lifetimes
43(4)
2.3 Relevant Prior Information: the Bayesian Approach
47(7)
2.3.1 Prior Information on Batch Quality
47(6)
2.3.2 Prior Attitudes about Component Lifetimes
53(1)
2.4 Costs and Consequences: Simple Decision Theory Ideas
54(8)
2.5 Comment and Comparisons
62(3)
Chapter
3. Probability
65(34)
3.1 Types of Probability
65(8)
3.2 'Classical' Probability
73(3)
3.3 The Frequency View
76(5)
3.4 Logical Probability
81(3)
3.5 Subjective Probability
84(8)
3.6 Other Viewpoints
92(4)
3.6.1 Chaos
92(2)
3.6.2 Fuzzy Set Theory
94(1)
3.6.3 Risk, Uncertainty and Sensitivity Analysis
95(1)
3.7 Some Historical Background
96(1)
3.8 And So ...
97(1)
3.9 And Yet ...
98(1)
Chapter
4. Utility and Decision-making
99(24)
4.1 Setting a Value on Rewards and Consequences
101(5)
4.2 The Rational Expression of Preferences
106(2)
4.3 Preferences for Prospects and Mixtures of Prospects
108(2)
4.4 The Numerical Assessment of Prospects
110(1)
4.5 The Measurement of Utilities
111(4)
4.5.1 Formal Construction of Utilities
111(2)
4.5.2 Personal Expression of Utilities
113(2)
4.6 Decision-making
115(1)
4.7 The Utility of Money
116(3)
4.8 Comment: Mathematical Refinements: Distinctions of Attitude
119(4)
Chapter
5. Classical Inference
123(78)
5.1 Basic Aims and Concepts
125(6)
5.1.1 Information and its Representation
127(4)
5.2 Estimation and Testing Hypotheses--the Dual Aims
131(6)
5.3 Point Estimation
137(28)
5.3.1 Criteria for Point Estimators
137(7)
5.3.2 Optimum Estimators
144(8)
5.3.3 Methods of Constructing Estimators
152(10)
5.3.4 Estimating Several Parameters
162(3)
5.4 Testing Statistical Hypotheses
165(16)
5.4.1 Criteria for Hypothesis Tests
166(5)
5.4.2 Uniformly Most Powerful Tests
171(6)
5.4.3 Construction of Tests
177(4)
5.5 Region and Interval Estimates
181(4)
5.6 Ancillarity, Conditionality, Modified forms of Sufficiency and Likelihood
185(6)
5.6.1 The Sufficiency, Conditionality and Likelihood Principles
186(3)
5.6.2 Modified Likelihood Forms (Marginal, Partial, Profile, etc.)
189(2)
5.7 Comment and Controversy
191(10)
5.7.1 Initial and Final Precision
192(2)
5.7.2 Prediction and Tolerance Regions
194(1)
5.7.3 Hypothesis Tests and Decisions
195(2)
5.7.4 Counter Criticism
197(4)
Chapter
6. Bayesian Inference
201(50)
6.1 Thomas Bayes
201(2)
6.2 The Bayesian Method
203(4)
6.3 Particular Techniques
207(10)
6.4 Prediction in Bayesian Inference
217(2)
6.5 Prior Information
219(16)
6.5.1 Prior Ignorance
220(5)
6.5.2 Vague Prior Knowledge
225(3)
6.5.3 Substantial Prior Knowledge
228(2)
6.5.4 Conjugate Prior Distributions
230(4)
6.5.5 Quantifying Subjective Prior Information
234(1)
6.6 Computing Posterior Distributions
235(3)
6.7 Empirical Bayes' methods: Meta-prior Distributions
238(4)
6.7.1 Empirical Bayes' Methods
238(2)
6.7.2 Meta-prior Distributions
240(2)
6.8 Comment and Controversy
242(9)
6.8.1 Interpretation of Prior and Posterior Distributions
242(3)
6.8.2 Sufficiency, Likelihood and Unbiasedness
245(2)
6.8.3 Controversy
247(4)
Chapter
7. Decision Theory
251(46)
7.1 An Illustrative Example
253(9)
7.2 Basic Concepts and Principles
262(7)
7.2.1 The Decision Theory Model
264(1)
7.2.2 The No-data Situation
264(1)
7.2.3 Sample Data
265(4)
7.3 Attainment and Implementation
269(17)
7.3.1 Admissibility and Unbiasedness
270(5)
7.3.2 Determination of Bayes' Decision Rules
275(3)
7.3.3 Minimax Decision Rules
278(1)
7.3.4 Estimation and Hypothesis Testing
279(7)
7.4 Problems with Finite Numbers of Actions, and States of Nature
286(3)
7.4.1 The No-data Problem
286(1)
7.4.2 The Use of Sample Data
287(2)
7.5 Extensions and Modifications
289(3)
7.6 Critical Comment
292(5)
Chapter
8. Other Approaches
297(34)
8.1 Fiducial Inference
298(8)
8.2 Likelihood Inference
306(5)
8.3 Plausibility Inference
311(2)
8.4 Structural Inference
313(6)
8.5 Pivotal Inference
319(3)
8.6 Information
322(3)
8.7 Causal Inference
325(1)
8.8 Prequential Inference
326(1)
8.9 Indeterminism and the 'Mathematics of Philosophy'
327(4)
Chapter
9. Perspective
331(6)
References 337(28)
Index 365


Vic Barnett is the author of Comparative Statistical Inference, 3rd Edition, published by Wiley.