Principles of Statistical Inference

by D. R. Cox

• ISBN13: 9780521685672
• ISBN10: 0521685672
• Edition: 1st
• Format: Paperback
• Copyright: 2006-08-21
• Publisher: Cambridge University Press

Summary

In this important book, D. R. Cox develops the key concepts of the 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. Continuing a 60-year career of contribution to statistical thought, Professor Cox is ideally placed to give the comprehensive, balanced account of the field that is now needed.

Table of Contents

List of examples	ix
Preface	xiii
1 Preliminaries	1	(16)
Summary	1	(1)
1.1 Starting point	1	(2)
1.2 Role of formal theory of inference	3	(1)
1.3 Some simple models	3	(4)
1.4 Formulation of objectives	7	(1)
1.5 Two broad approaches to statistical inference	7	(3)
1.6 Some further discussion	10	(3)
1.7 Parameters	13	(1)
Notes 1	14	(3)
2 Some concepts and simple applications	17	(13)
Summary	17	(1)
2.1 Likelihood	17	(1)
2.2 Sufficiency	18	(2)
2.3 Exponential family	20	(3)
2.4 Choice of priors for exponential family problems	23	(1)
2.5 Simple frequentist discussion	24	(1)
2.6 Pivots	25	(2)
Notes 2	27	(3)
3 Significance tests	30	(15)
Summary	30	(1)
3.1 General remarks	30	(1)
3.2 Simple significance test	31	(4)
3.3 One- and two-sided tests	35	(1)
3.4 Relation with acceptance and rejection	36	(1)
3.5 Formulation of alternatives and test statistics	36	(4)
3.6 Relation with interval estimation	40	(1)
3.7 Interpretation of significance tests	41	(1)
3.8 Bayesian testing	42	(1)
Notes 3	43	(2)
4 More complicated situations	45	(19)
Summary	45	(1)
4.1 General remarks	45	(1)
4.2 General Bayesian formulation	45	(2)
4.3 Frequentist analysis	47	(3)
4.4 Some more general frequentist developments	50	(9)
4.5 Some further Bayesian examples	59	(3)
Notes 4	62	(2)
5 Interpretations of uncertainty	64	(32)
Summary	64	(1)
5.1 General remarks	64	(1)
5.2 Broad roles of probability	65	(1)
5.3 Frequentist interpretation of upper limits	66	(2)
5.4 Neyman—Pearson operational criteria	68	(1)
5.5 Some general aspects of the frequentist approach	68	(1)
5.6 Yet more on the frequentist approach	69	(2)
5.7 Personalistic probability	71	(2)
5.8 Impersonal degree of belief	73	(3)
5.9 Reference priors	76	(2)
5.10 Temporal coherency	78	(1)
5.11 Degree of belief and frequency	79	(1)
5.12 Statistical implementation of Bayesian analysis	79	(5)
5.13 Model uncertainty	84	(1)
5.14 Consistency of data and prior	85	(1)
5.15 Relevance of frequentist assessment	85	(3)
5.16 Sequential stopping	88	(3)
5.17 A simple classification problem	91	(2)
Notes 5	93	(3)
6 Asymptotic theory	96	(37)
Summary	96	(1)
6.1 General remarks	96	(1)
6.2 Scalar parameter	97	(10)
6.3 Multidimensional parameter	107	(2)
6.4 Nuisance parameters	109	(5)
6.5 Tests and model reduction	114	(3)
6.6 Comparative discussion	117	(2)
6.7 Profile likelihood as an information summarizer	119	(1)
6.8 Constrained estimation	120	(4)
6.9 Semi-asymptotic arguments	124	(1)
6.10 Numerical-analytic aspects	125	(3)
6.11 Higher-order asymptotics	128	(2)
Notes 6	130	(3)
7 Further aspects of maximum likelihood	133	(28)
Summary	133	(1)
7.1 Multimodal likelihoods	133	(2)
7.2 Irregular form	135	(4)
7.3 Singular information matrix	139	(2)
7.4 Failure of model	141	(1)
7.5 Unusual parameter space	142	(2)
7.6 Modified likelihoods	144	(15)
Notes 7	159	(2)
8 Additional objectives	161	(17)
Summary	161	(1)
8.1 Prediction	161	(1)
8.2 Decision analysis	162	(1)
8.3 Point estimation	163	(6)
8.4 Non-likelihood-based methods	169	(6)
Notes 8	175	(3)
9 Randomization-based analysis	178	(16)
Summary	178	(1)
9.1 General remarks	178	(1)
9.2 Sampling a finite population	179	(5)
9.3 Design of experiments	184	(8)
Notes 9	192	(2)
Appendix A: A brief history	194	(3)
Appendix B: A personal view	197	(4)
References	201	(8)
Author index	209	(4)
Subject index	213