This book aims to provide a concise but comprehensive account of the essential elements of statistical inference and theory. It is designed to be used as a text for courses on statistical theory for students of mathematics or statistics at the advanced undergraduate or Masters level (UK) or the first-year graduate level (US), or as a reference for researchers in other fields seeking a concise treatment of the key concepts of and approaches to statistical inference. It is intended to give a contemporary and accessible account of procedures used to draw formal inference from data.

The book focusses on a clear presentation of the main concepts and results underlying different frameworks of inference, with particular emphasis on the contrasts among frequentist, Fisherian and Bayesian approaches. It provides a description of basic material on these main approaches to inference, as well as more advanced material on recent developments in statistical theory, including higher-order likelihood inference, bootstrap methods, conditional inference and predictive inference. It places particular emphasis on contemporary computational ideas, such as applied in bootstrap methodology and Markov chain Monte Carlo techniques of Bayesian inference. Throughout, the text concentrates on concepts, rather than mathematical detail, but every effort has been made to present the key theoretical results in as precise and rigorous a manner as possible, consistent with the overall mathematical level of the book. The book contains numerous extended examples of application of contrasting inference techniques to real data, as well as selected historical commentaries. Each chapter concludes with an accessible set of problems and exercises.