Comparative Statistical Inference

✍ Scribed by Vic Barnett

• Publisher: Wiley
• Year: 1999
• Tongue: English
• Leaves: 411
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover
Title
Contents
Preface
Preface to Second Edition
Preface to Third Edition
Acknowledgements
Chapter 1. Introduction: Statistical Inference and Decision-making
1.1 What is Statistics?
1.2 Probability Models
1.3 Relevant Information
1.4 Statistical Inference and Decision-making
1.5 Different Approaches
1.6 Arbitrariness and Controversy
1.7 Historical Comment and Further References
Chapter 2. An Illustration of the Different Approaches
2.1 A Practical Example
2.2 Sample Data as the Sole Source of Information: the Classical Approach
2.2.1 Batch Quality
2.2.2 Component Lifetimes
2.3 Relevant Prior Information: the Bayesian Approach
2.3.1 Prior Information on Batch Quality
2.3.2 Prior Attitudes about Component Lifetimes
2.4 Costs and Consequences: Simple Decision Theory Ideas
2.5 Comment and Comparisons
Chapter 3. Probability
3.1 Types of Probability
3.2 'Classical' Probability
3.3 The Frequency View
3.4 Logical Probability
3.5 Subjective Probability
3.6 Other Viewpoints
3.6.1 Chaos
3.6.2 Fuzzy Set Theory
3.6.3 Risk, Uncertainty and Sensitivity Analysis
3.7 Some Historical Background
3.8 And So …
3.9 And Yet …
Chapter 4. Utility and Decision-making
4.1 Setting a Value on Rewards and Consequences
4.2 The Rational Expression of Preferences
4.3 Preferences for Prospects and Mixtures of Prospects
4.4 The Numerical Assessment of Prospects
4.5 The Measurement of Utilities
4.5.1 Formal Construction of Utilities
4.5.2 Personal Expression of Utilities
4.6 Decision-making
4.7 The Utility of Money
4.8 Comment: Mathematical Refinements: Distinctions of Attitude
Chapter 5. Classical Inference
5.1 Basic Aims and Concepts
5.1.1 Information and its Representation
5.2 Estimation and Testing Hypotheses—the Dual Aims
5.3 Point Estimation
5.3.1 Criteria for Point Estimators
5.3.2 Optimum Estimators
5.3.3 Methods of Constructing Estimators
5.3.4 Estimating Several Parameters
5.4 Testing Statistical Hypotheses
5.4.1 Criteria for Hypothesis Tests
5.4.2 Uniformly Most Powerful Tests
5.4.3 Construction of Tests
5.5 Region and Interval Estimates
5.6 Ancillarity, Conditionality, Modified forms of Sufficiency and Likelihood
5.6.1 The Sufficiency, Conditionality and Likelihood Principles
5.6.2 Modified Likelihood Forms (Marginal, Partial, Profile, etc.)
5.7 Comment and Controversy
5.7.1 Initial and Final Precision
5.7.2 Prediction and Tolerance Regions
5.7.3 Hypothesis Tests and Decisions
5.7.4 Counter Criticism
Chapter 6. Bayesian Inference
6.1 Thomas Bayes
6.2 The Bayesian Method
6.3 Particular Techniques
6.4 Prediction in Bayesian Inference
6.5 Prior Information
6.5.1 Prior Ignorance
6.5.2 Vague Prior Knowledge
6.5.3 Substantial Prior Knowledge
6.5.4 Conjugate Prior Distributions
6.5.5 Quantifying Subjective Prior Information
6.6 Computing Posterior Distributions
6.7 Empirical Bayes' methods: Meta-prior Distributions
6.7.1 Empirical Bayes' Methods
6.7.2 Meta-prior Distributions
6.8 Comment and Controversy
6.8.1 Interpretation of Prior and Posterior Distributions
6.8.2 Sufficiency, Likelihood and Unbiasedness
6.8.3 Controversy
Chapter 7. Decision Theory
7.1 An Illustrative Example
7.2 Basic Concepts and Principles
7.2.1 The Decision Theory Model
7.2.2 The No-data Situation
7.2.3 Sample Data
7.3 Attainment and Implementation
7.3.1 Admissibility and Unbiasedness
7.3.2 Determination of Bayes' Decision Rules
7.3.3 Minimax Decision Rules
7.3.4 Estimation and Hypothesis Testing
7.4 Problems with Finite Numbers of Actions, and States of Nature
7.4.1 The No-data Problem
7.4.2 The Use of Sample Data
7.5 Extensions and Modifications
7.6 Critical Comment
Chapter 8. Other Approaches
8.1 Fiducial Inference
8.2 Likelihood Inference
8.3 Plausibility Inference
8.4 Structural Inference
8.5 Pivotal Inference
8.6 Information
8.7 Causal Inference
8.8 Prequential Inference
8.9 Indeterminism and the 'Mathematics of Philosophy'
Chapter 9. Perspective
References
Index
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