Applied Statistical Inference
Likelihood and Bayes
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Beschreibung
This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective.
A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.
This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective.
A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.
Offers a non-technical introduction to model-based likelihood and Bayesian inference Covers many applications illustrating the concepts and approaches Complemented by exercises at the end of each chapter, accompanied by an online solutions manual Complete with program examples in the open-source software R Includes a comprehensive appendix covering the necessary mathematical prerequisites Includes supplementary material: sn.pub/extras
Autor*in
Leonhard Held
Themen in »Applied Statistical Inference«
Bayesian Inference Likelihood Inference Model Choice Prediction
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From the book reviews:
“The book by Leonhard Held and Daniel Sabanés Bové is highly recommended for anyone who is interested in acquainting themselves with or extending their knowledge of likelihood-based and Bayesian inference. This will certainly include Bachelor and Master students with a quantitative focus, but also researchers who are interested in getting to know the background of many modern inferential procedures in more detail.” (Thomas Kneib, Biometrical Journal, October, 2014)
“Modern statistical techniques for likelihood and Bayesian approaches are presented in detail throughout the book. … The intended audience is formed by students in bioinformatics, biomathematics, etc., but a large audience could be interested in this book.” (Marina Gorunescu, zbMATH, Vol. 1281, 2014)
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