Comparative Statistical Inference

by Barnett, Vic

• ISBN13: 9780471976431
• ISBN10: 0471976431
• Edition: 3rd
• Format: Hardcover
• Copyright: 1999-08-03
• Publisher: WILEY

Summary

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. 'ˆ— Includes fully updated and revised material from the successful second edition 'ˆ— Recent changes in emphasis, principle and methodology are carefully explained and evaluated 'ˆ— Discusses all recent major developments 'ˆ— Particular attention is given to the nature and importance of basic concepts (probability, utility, likelihood etc) 'ˆ— 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.

Author Biography

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

Table of Contents

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