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PRINTED BOOKS
Author Cox, D. R. (David Roxbee)

Title Principles of statistical inference / D.R. Cox.

Published Cambridge ; New York : Cambridge University Press, 2006.

Copies

Location Call No. Status
 UniM Bund  519.54 COX {Bund89 20200519}    AVAILABLE
Physical description xv, 219 pages : illustrations ; 23 cm
Bibliography Includes bibliographical references (pages 201-208) and indexes.
Contents 1.1 Starting point 1 -- 1.2 Role of formal theory of inference 3 -- 1.3 Some simple models 3 -- 1.4 Formulation of objectives 7 -- 1.5 Two broad approaches to statistical inference 7 -- 1.6 Some further discussion 10 -- 1.7 Parameters 13 -- 2 Some concepts and simple applications 17 -- 2.1 Likelihood 17 -- 2.2 Sufficiency 18 -- 2.3 Exponential family 20 -- 2.4 Choice of priors for exponential family problems 23 -- 2.5 Simple frequentist discussion 24 -- 2.6 Pivots 25 -- 3 Significance tests 30 -- 3.2 Simple significance test 31 -- 3.3 One- and two-sided tests 35 -- 3.4 Relation with acceptance and rejection 36 -- 3.5 Formulation of alternatives and test statistics 36 -- 3.6 Relation with interval estimation 40 -- 3.7 Interpretation of significance tests 41 -- 3.8 Bayesian testing 42 -- 4 More complicated situations 45 -- 4.2 General Bayesian formulation 45 -- 4.3 Frequentist analysis 47 -- 4.4 Some more general frequentist developments 50 -- 4.5 Some further Bayesian examples 59 -- 5 Interpretations of uncertainty 64 -- 5.2 Broad roles of probability 65 -- 5.3 Frequentist interpretation of upper limits 66 -- 5.4 Neyman-Pearson operational criteria 68 -- 5.5 Some general aspects of the frequentist approach 68 -- 5.6 Yet more on the frequentist approach 69 -- 5.7 Personalistic probability 71 -- 5.8 Impersonal degree of belief 73 -- 5.9 Reference priors 76 -- 5.10 Temporal coherency 78 -- 5.11 Degree of belief and frequency 79 -- 5.12 Statistical implementation of Bayesian analysis 79 -- 5.13 Model uncertainty 84 -- 5.14 Consistency of data and prior 85 -- 5.15 Relevance of frequentist assessment 85 -- 5.16 Sequential stopping 88 -- 5.17 A simple classification problem 91 -- 6 Asymptotic theory 96 -- 6.2 Scalar parameter 97 -- 6.3 Multidimensional parameter 107 -- 6.4 Nuisance parameters 109 -- 6.5 Tests and model reduction 114 -- 6.6 Comparative discussion 117 -- 6.7 Profile likelihood as an information summarizer 119 -- 6.8 Constrained estimation 120 -- 6.9 Semi-asymptotic arguments 124 -- 6.10 Numerical-analytic aspects 125 -- 6.11 Higher-order asymptotics 128 -- 7 Further aspects of maximum likelihood 133 -- 7.1 Multimodal likelihoods 133 -- 7.2 Irregular form 135 -- 7.3 Singular information matrix 139 -- 7.4 Failure of model 141 -- 7.5 Unusual parameter space 142 -- 7.6 Modified likelihoods 144 -- 8 Additional objectives 161 -- 8.1 Prediction 161 -- 8.2 Decision analysis 162 -- 8.3 Point estimation 163 -- 8.4 Non-likelihood-based methods 169 -- 9 Randomization-based analysis 178 -- 9.2 Sampling a finite population 179 -- 9.3 Design of experiments 184 -- Appendix A A brief history 194 -- Appendix B A personal view 197.
Subject Mathematical statistics.
Probabilities.
Standard Number 9780521866736
9780521685672
ISBN 0521685672 (paperback)
0521866731 (hbk.)
9780521685672 (paperback)
9780521866736 (hbk.)