Principles of statistical inference

In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses. In This Definitive Book, D.r. Cox Gives A Comprehensive And Balanced Appraisal Of Statistical Inference. He Develops The Key Concepts, Describing And Comparing The Main Ideas And Controversies Over Foundational Issues That Have Been Keenly Argued For More Than Two-hundred Years. Continuing A Sixty-year Career Of Major Contributions To Statistical Thought, No One Is Better Placed To Give This Much-needed Account Of The Field. An Appendix Gives A More Personal Assessment Of The Merits Of Different Ideas. The Content Ranges From The Traditional To The Contemporary. While Specific Applications Are Not Treated, The Book Is Strongly Motivated By Applications Across The Sciences And Associated Technologies. The Mathematics Is Kept As Elementary As Feasible, Though Previous Knowledge Of Statistics Is Assumed. The Book Will Be Valued By Every User Or Student Of Statistics Who Is Serious About Understanding The Uncertainty Inherent In Conclusions From Statistical Analyses. List Of Examples -- Preface -- 1. Preliminaries -- Summary -- 1.1. Starting Point -- 1.2. Role Of Formal Theory Of Inference -- 1.3. Some Simple Models -- 1.4. Formulation Of Objectives -- 1.5. Two Broad Approaches To Statistical Inference -- 1.6. Some Further Discussion -- 1.7. Parameters -- Notes 1 -- 2. Some Concepts And Simple Applications -- Summary -- 2.1. Likelihood -- 2.2. Sufficiency -- 2.3. Exponential Family -- 3.4. Choice Of Priors For Exponential Family Problems -- 2.5. Simple Frequentist Discussion -- 2.6. Pivots -- Notes 2 -- 3. Significance Tests -- Summary -- 3.1. General Remarks -- 3.2. Simple Significance Test -- 3.3. One- And Two-sided Tests -- 3.4. Relation With Acceptance And Rejection -- 3.5. Formulation Of Alternatives And Test Statistics -- 3.6. Relation With Interval Estimation -- 3.7. Interpretation Of Significance Tests -- 3.8. Bayesian Testing -- Notes 3. 4. More Complicated Situations -- Summary -- 4.1. General Remarks -- 4.2. General Bayesian Formulation -- 4.3. Frequentist Analysis -- 4.4. Some More General Frequentist Developments -- 4.5. Some Further Bayesian Examples -- Notes 4 -- 5. Interpretations Of Uncertainty -- Summary -- 5.1. General Remarks -- 5.2. Broad Roles Of Probability-- 5.3. Frequentist Interpretation Of Upper Limits -- 5.4. Neyman-pearson Operational Criteria -- 5.5. Some General Aspects Of The Frequentist Approach -- 5.6. Yet More On The Frequentist Approach -- 5.7. Personalistic Probability -- 5.8. Impersonal Degree Of Belief -- 5.9. Reference Priors -- 5.10. Temporal Coherency -- 5.11. Degree Of Belief And Frequency -- 5.12. Statistical Implementation Of Bayesian Analysis -- 5.13. Model Uncertainty -- 5.14. Consistency Of Data And Prior -- 5.15. Relevance Of Frequentist Assessment -- 1.16. Sequential Stopping -- 5.17. A Simple Classification Problem -- Notes 5 -- 6. Asymptotic Theory -- Summary -- 6.1. General Remarks -- 6.2. Scalar Parameter -- 6.3. Multidimensional Parameter -- 6.4. Nuisance Parameters -- 6.5. Tests And Model Reduction -- 6.6. Comparative Discussion -- 6.7. Profile Likelihood As An Information Summarizer -- 6.8. Constrained Estimation -- 6.9. Semi-asymptotic Arguments -- 6.10. Numerical-analytic Aspects -- 6.11. Higher-order Asymptotics -- Notes 6. 7. Further Aspects Of Maximum Likelihood -- Summary -- 7.1. Multimodal Likelihoods -- 7.2. Irregular Form -- 7.3. Singular Information Matrix -- 7.4. Failure Of Model -- 7.5. Unusual Parameter Space -- 7.6. Modified Likelihoods -- Notes 7 -- 8. Additional Objectives -- Summary -- 8.1. Prediction -- 8.2. Decision Analysis -- 8.3. Point Estimation -- 8.4. Non-likelihood-based Methods -- Notes 8 -- 9. Randomization-based Analysis -- Summary -- 9.1. General Remarks -- 9.2. Sampling A Finite Population -- 9.3. Design Of Experiments -- Notes 9 -- Appendix A : A Brief History-- Appendix B : A Personal View -- References -- Author Index -- Subject Index. D.r. Cox. Includes Bibliographical References (p. 201-208) And Indexes. "D.R. Cox develops the key concepts of theory of statistical inference, in particular describing and comparing the main ideas and controversies over foundational issues that have rumbled on for more than 200 years. The careful comparison of frequentist and Bayesian approaches to inference allows readers to form their own opinion of the advantages and disadvantages. Two appendices give a brief historical overview and the author's more personal assessment of the merits of different ideas." The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The underlying mathematics is kept as elementary as feasible, though some previous knowledge of statistics is assumed. This book is for every serious user or student of statistics - in particular, for anyone wanting to understand the uncertainty inherent in conclusions from statistical analyses.