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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.

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.

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.

This is the second edition of a monograph on generalized linear models with random effects that extends the classic work of McCullagh and Nelder. It has been thoroughly updated, with around 80 pages added, including new material on the extended likelihood approach that strengthens the theoretical basis of the methodology, new developments in variable selection and multiple testing, and new examples and applications. It includes an R package for all the methods and examples that supplement the book.

Unlike mathematics, statistics deals with real-world data and involves a higher degree of subjectivity due to the role of interpretation. Interpretation is shaped by context as well as the knowledge, preferences, assumptions and preconceptions of the interpreter, leading to a variety of interpretations of concepts as well as results. Philosophies, Puzzles and Paradoxes: A Statistician’s Search for Truth thoroughly examines the distinct philosophical approaches to statistics – Bayesian, frequentist and likelihood – arising from different interpretations of probability and uncertainty. These differences are highlighted through numerous puzzles and paradoxes and illuminated by extensive discussions of the background philosophy of science.Features:Exploration of the philosophy of knowledge and truth and how they relate to deductive and inductive reasoning, and ultimately scientific and statistical thinkingDiscussion of the philosophical theories of probability that are wider than the standard Bayesian and frequentist viewsExposition and examination of Savage’s axioms as the basis of subjective probability and Bayesian statisticsExplanation of likelihood and likelihood-based inference, including the controversy surrounding the likelihood principleDiscussion of fiducial probability and its evolution to confidence procedureIntroduction of extended and hierarchical likelihood for random parameters, with the recognition of confidence as extended likelihood, leading to epistemic confidence as an objective measure of uncertainty for single eventsDetailed analyses and new variations of classic paradoxes, such as the Monty Hall puzzle, the paradox of the ravens, the exchange paradox, and moreSubstantive yet non-technical, catering to readers with only introductory exposure to the theory of probability and statisticsThis book primarily targets statisticians in general, including both undergraduate and graduate students, as well as researchers interested in the philosophical basis of probability and statistics. It is also suitable for philosophers of science and general readers intrigued by puzzles and paradoxes.

Unlike mathematics, statistics deals with real-world data and involves a higher degree of subjectivity due to the role of interpretation. Interpretation is shaped by context as well as the knowledge, preferences, assumptions and preconceptions of the interpreter, leading to a variety of interpretations of concepts as well as results. Philosophies, Puzzles and Paradoxes: A Statistician’s Search for Truth thoroughly examines the distinct philosophical approaches to statistics – Bayesian, frequentist and likelihood – arising from different interpretations of probability and uncertainty. These differences are highlighted through numerous puzzles and paradoxes and illuminated by extensive discussions of the background philosophy of science.Features:Exploration of the philosophy of knowledge and truth and how they relate to deductive and inductive reasoning, and ultimately scientific and statistical thinkingDiscussion of the philosophical theories of probability that are wider than the standard Bayesian and frequentist viewsExposition and examination of Savage’s axioms as the basis of subjective probability and Bayesian statisticsExplanation of likelihood and likelihood-based inference, including the controversy surrounding the likelihood principleDiscussion of fiducial probability and its evolution to confidence procedureIntroduction of extended and hierarchical likelihood for random parameters, with the recognition of confidence as extended likelihood, leading to epistemic confidence as an objective measure of uncertainty for single eventsDetailed analyses and new variations of classic paradoxes, such as the Monty Hall puzzle, the paradox of the ravens, the exchange paradox, and moreSubstantive yet non-technical, catering to readers with only introductory exposure to the theory of probability and statisticsThis book primarily targets statisticians in general, including both undergraduate and graduate students, as well as researchers interested in the philosophical basis of probability and statistics. It is also suitable for philosophers of science and general readers intrigued by puzzles and paradoxes.