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Informationen zum Autor Russell B. Millar is the author of Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB, published by Wiley. Klappentext This book takes a fresh look at the popular and well-established method of maximum likelihood for statistical estimation and inference. It begins with an intuitive introduction to the concepts and background of likelihood, and moves through to the latest developments in maximum likelihood methodology, including general latent variable models and new material for the practical implementation of integrated likelihood using the free ADMB software. Fundamental issues of statistical inference are also examined, with a presentation of some of the philosophical debates underlying the choice of statistical paradigm.Key features:* Provides an accessible introduction to pragmatic maximum likelihood modelling.* Covers more advanced topics, including general forms of latent variable models (including non-linear and non-normal mixed-effects and state-space models) and the use of maximum likelihood variants, such as estimating equations, conditional likelihood, restricted likelihood and integrated likelihood.* Adopts a practical approach, with a focus on providing the relevant tools required by researchers and practitioners who collect and analyze real data.* Presents numerous examples and case studies across a wide range of applications including medicine, biology and ecology.* Features applications from a range of disciplines, with implementation in R, SAS and/or ADMB.* Provides all program code and software extensions on a supporting website.* Confines supporting theory to the final chapters to maintain a readable and pragmatic focus of the preceding chapters.This book is not just an accessible and practical text about maximum likelihood, it is a comprehensive guide to modern maximum likelihood estimation and inference. It will be of interest to readers of all levels, from novice to expert. It will be of great benefit to researchers, and to students of statistics from senior undergraduate to graduate level. For use as a course text, exercises are provided at the end of each chapter. Zusammenfassung Applied Likelihood Methods provides an accessible and practical introduction to likelihood modeling, supported by examples and software. The book features applications from a range of disciplines, including statistics, medicine, biology, and ecology. Inhaltsverzeichnis Preface xiii Part I PRELIMINARIES 1 1 A taste of likelihood 3 1.1 Introduction 3 1.2 Motivating example 4 1.3 Using SAS, R and ADMB 9 1.4 Implementation of the motivating example 11 1.5 Exercises 17 2 Essential concepts and iid examples 18 2.1 Introduction 18 2.2 Some necessary notation 19 2.3 Interpretation of likelihood 23 2.4 IID examples 25 2.5 Exercises 33 Part II PRAGMATICS 37 3 Hypothesis tests and confidence intervals or regions 39 3.1 Introduction 39 3.2 Approximate normality of MLEs 40 3.3 Wald tests, confidence intervals and regions 43 3.4 Likelihood ratio tests, confidence intervals and regions 49 3.5 Likelihood ratio examples 54 3.6 Profile likelihood 57 3.7 Exercises 59 4 What you really need to know 64 4.1 Introduction 64 4.2 Inference about g ( ¿ ) 65 4.3 Wald statistics - quick and dirty? 75 4.4 Model selection 79 4.5 Bootstrapping 81 4.6 Prediction 91 4.7 Things that can mess you up 95 4.8 Exercises 98 5 Maximizing the likelihood 101 5.1 Introduction 101 5.2 The Newton-Raphson algorithm 103 5.3 The EM (Expectation-Maximization) algorithm 104 5.4 Multi-stage maximization 113 5.5 Exercises 118 6 Some widely us...
