In this ground-breaking work, Peter Walley constructs and justifies a radically rational theory of statistical inference. He derives, from fundamental principles, new statistical methods that are coherent and objective and correct crucial failings of standard methods. Volume 1 presents the foundations and the general theory of statistical inference. Volume 2 applies the theory to derive practical methods for analysing common types of statistical data. The book unifies the wide-ranging, highly original research produced by the author during 1980-2005, most of which has been unpublished until now. The methodology developed in the book provides a general, systematic and coherent way to analyse statistical problems. The methods apply to all kinds of statistical problem and all types of data; inference about parameters, predictive inference, and nonparametric inference; informative or uninformative prior models; point estimation, interval estimation, hypothesis testing, density estimation, and statistical decision problems. They also enable a unified treatment of robustness. The book should be of great interest to everyone who uses or studies statistical inference. The results have profound implications for a wide range of disciplines in which statistical methods are important, including econometrics, decision theory, inductive logic, philosophy of science, psychology, and clinical trials.