Statistical and Inductive Inference by Minimum Message Length

The Minimum Message Length (MML) Principle is an information-theoretic approach to induction, hypothesis testing, model selection, and statistical inference. MML, which provides a formal specification for the implementation of Occam's Razor, asserts that the best explanation of observed data is the shortest. Further, an explanation is acceptable (i.e. the induction is justified) only if the explanation is shorter than the original data.

This book gives a sound introduction to the Minimum Message Length Principle and its applications, provides the theoretical arguments for the adoption of the principle, and shows the development of certain approximations that assist its practical application. MML appears also to provide both a normative and a descriptive basis for inductive reasoning generally, and scientific induction in particular. The book describes this basis and aims to show its relevance to the Philosophy of Science.

Statistical and Inductive Inference by Minimum Message Length will be of special interest to graduate students and researchers in Machine Learning and Data Mining, scientists and analysts in various disciplines wishing to make use of computer techniques for hypothesis discovery, statisticians and econometricians interested in the underlying theory of their discipline, and persons interested in the Philosophy of Science. The book could also be used in a graduate-level course in Machine Learning and Estimation and Model-selection, Econometrics and Data Mining.
From the reviews:

"Any statistician interested in the foundations of the discipline, or the deeper philosophical issues of inference, will find this volume a rewarding read." Short Book Reviews of the International Statistical Institute, December 2005

"This very significant monograph covers the topic of the Minimum Message Length (MML) principle, a new approach to induction, hypothesis testing, model selection, and statistical inference. This valuable book covers the topics at a level suitable for professionals and graduate students in Statistics, Computer Science, Data Mining, Machine Learning, Estimation and Model-selection, Econometrics etc." (Jerzy Martyna, Zentralblatt MATH, Vol. 1085, 2006)

"This book is around a simple idea: The best explanation of the facts is the shortest. The book applies the above idea to statistical estimation in a Bayesian context. I think it will be valuable for readers who have at the same time strong interest in Bayesian decision theory and in Shannon information theory." (Michael Kohler, Metrika, Vol. 64, 2006)