Likelihood and Bayesian Inference

This book covers statistical inference based on the likelihood function. Discusses frequentist likelihood-based inference from a Fisherian viewpoint, Bayesian inference techniques including point and interval estimates, model choice and prediction and more.

This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, 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. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book Applied Statistical Inference has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.

Offers an easily accessible and comprehensive introduction to model-based statistical inference Provides real-world applications in biology, medicine and epidemiology with programming examples in the open-source software R Includes exercises at the end of each chapter, for which solutions are available on the website Includes a comprehensive appendix covering the necessary mathematical background and various R-programming tips

Auteur

Leonhard Held is a Full Professor of Biostatistics, Director of the Master's Program in Biostatistics and Chair of the Center for Reproducible Science at the University of Zurich, Switzerland. He has published several books and numerous articles on statistical methodology, applied statistics and biomedical research and teaches undergraduate and graduate-level courses in Biostatistics and Medical Statistics.

Daniel Sabanés Bové completed his PhD in Statistics at the University of Zurich under the supervision of Leonhard Held. He started his career as a biostatistician in oncology drug development at Hoffmann-La Roche in 2013, and has been a data scientist at Google since 2018.

Contenu