Essentials Of Statistical Inference

Preface

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.

Prerequisites for the book are calculus, linear algebra and some knowledge of basic

probability (including ideas such as conditional probability, transformations of densities

etc., though not measure theory). Some previous familiarity with the objectives of and

main approaches to statistical inference is helpful, but not essential. Key mathematical and

probabilistic ideas are reviewed in the text where appropriate.