Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood. In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Cover)......Page 1 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Contents)......Page 10 In_All_Likelihood_Statistical_Modelling_and_Infere-1......Page 16 In_All_Likelihood_Statistical_Modelling_and_Infere...-2......Page 36 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_3......Page 68 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_4......Page 88 In_All_Likelihood_Statistical_Modelling_and_Infere..._---5......Page 132 In_All_Likelihood_Statistical_Modelling_and_Infere..._----6......Page 164 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_7......Page 208 In_All_Likelihood_Statistical_Modelling_and_Infere..._--8......Page 228 In_All_Likelihood_Statistical_Modelling_and_Infere..._---9......Page 246 In_All_Likelihood_Statistical_Modelling_and_Infere..._-10......Page 288 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(11_Complex_data_structures)......Page 312 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(12_EM_Algorithm)......Page 356 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(13_Robustness_of_likelihood_specification)......Page 380 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(14_Estimating_equations_and_quasi-likelihood)......Page 400 In_All_Likelihood_Statistical_Modelling_and_Infere..._---15......Page 424 In_All_Likelihood_Statistical_Modelling_and_Infere..._--16......Page 440 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(17_Random_and_mixed_effects_models)......Page 450 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(18_Nonparametric_smoothing)......Page 488 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Bibliography)......Page 518 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Index)......Page 530 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Cover) 1 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Contents) 10 likelihood1-10 16 likelihood1-7 16 In_All_Likelihood_Statistical_Modelling_and_Infere-1 16 In_All_Likelihood_Statistical_Modelling_and_Infere...-2 36 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_3 68 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_4 88 In_All_Likelihood_Statistical_Modelling_and_Infere..._---5 132 In_All_Likelihood_Statistical_Modelling_and_Infere..._----6 164 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_7 208 In_All_Likelihood_Statistical_Modelling_and_Infere..._--8 228 In_All_Likelihood_Statistical_Modelling_and_Infere..._---9 246 In_All_Likelihood_Statistical_Modelling_and_Infere..._-10 288 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(11_Complex_data_structures) 312 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(12_EM_Algorithm) 356 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(13_Robustness_of_likelihood_specification) 380 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(14_Estimating_equations_and_quasi-likelihood) 400 In_All_Likelihood_Statistical_Modelling_and_Infere..._---15 424 In_All_Likelihood_Statistical_Modelling_and_Infere..._--16 440 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(17_Random_and_mixed_effects_models) 450 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(18_Nonparametric_smoothing) 488 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Bibliography) 518 In_All_Likelihood_Statistical_Modelling_and_Infere..._----_(Index) 530 This book presents the role of likelihood in a whole range of statistical problems, from a simple comparison of two accident rates to complex studies requiring generalized linear or semiparametric modeling. The book emphasizes that the likelihood is not simply a device to produce an estimate, but more importantly it is a tool for modeling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With currently available computing power, examples are not contrived to allow a closed analytical solution, and the book concentrates on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models, generalized linear mixed models, nonparametric smoothing, robustness, EM algorithm and empirical likelihood. --back cover
This text concentrates on what can be achieved using the likelihood/Fisherian methods of taking into account uncertainty when studying a statistical problem. It takes the concept of the likelihood as the best method for unifying the demands of statistical modeling and theory of inference. Every likelihood concept is illustrated with realistic examples ranging from a simple comparison of two accident rates to complex studies that require generalized linear or semiparametric modeling. The emphasis is on likelihood not as just a device used to produce an estimate, but as an important tool for modeling.
