In All Likelihood Statistical Modelling and Inference Using Likelihood

This new, updated second edition of In All Likelihood explores the central role of likelihood in a wide spectrum of statistical problems, ranging from simple comparisons-such as evaluating accident rates between two groups-to sophisticated analyses involving generalized linear models and semiparametric methods. Rather than treating likelihood merely as a tool for point estimation, the book highlights its broader value as a foundational framework for constructing, understanding and computational implementation of statistical models. It emphasizes how likelihood perspectives inform model development, assessment, and inference in a cohesive and intuitive way. While grounded in essential mathematical theory, the book adopts an informal and accessible approach, using heuristic reasoning and illustrative, realistic examples to convey key ideas. It avoids overly contrived problems that yield to theoretically clean and closed-form solutions, instead embracing more realistic and complex real-world data analysis made tractable by modern computing resources. This perspective helps focus attention on the statistical reasoning behind model choice and interpretation. The text also integrates a wide range of modern topics that extend classical likelihood theory, including generalized and hierarchical generalized linear models, nonparametric smoothing techniques, robust methods, the EM algorithm, and empirical likelihood. Suitable for students, researchers, and practitioners, this book provides both foundational insights and contemporary perspectives on likelihood-based statistical modelling.

1 - Introduction
2 - Elements of likelihood in inference
3 - More properties of likelihood
4 - Basic models and simple applications
5 - Frequentist properties
6 - Modelling relationships: regression models
7 - Evidence and the likelihood principle*
8 - Score function and Fisher information
9 - Large-sample results
10 - Dealing with nuisance parameters
11 - Complex data structures
12 - EM Algorithm
13 - Robustness of likelihood specification
14 - Estimating equations and quasi-likelihood
15 - Empirical likelihood
16 - Likelihood of random parameters
17 - Random and mixed effects models
18 - Nonparametric smoothing

Yudi Pawitan graduated with a PhD in Statistics in 1987 from the University of California at Davis and has been Professor of Biostatistics since 2001 at the Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden. He has worked in many areas of statistical applications, including time series analyses, medical imaging, and modelling and analysis of high-throughput molecular data. He has published more than 200 peer-reviewed research papers, split about equally between methodology and applied publications. He is co-author of the monograph Generalized Linear Models with Random Effects (2017) together with Youngjo Lee and John Nelder, which covers likelihood-based statistical modelling and inference in hierarchical GLMs. More recently, together with Youngjo Lee, he published Philosophies, Puzzles and Paradoxes, a book on statistical philosophy.