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No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Introduction.- Shannon-Wiener information.- Coding with random processes.- Universal coding.- Kolmogorov complexity.- Stochastic complexity.- Structure function.- The MDL principle.- Applications.
From the reviews: "Readership: Graduate students and researchers in statistics, computer science and engineering, anyone interested in statistical modelling. This book presents a personal introduction to statistical modelling based on the principle that the objective of modelling is to extract learnable information from data with suggested classes of probability models. It grew from lectures to doctoral students ! and retains much of the economical style of a lecture series. ! Therefore, this fascinating volume offers an excellent source of important statistical research problems calling for solution." (Erkki P. Liski, International Statistical Review, Vol. 75 (2), 2007) "This book covers the minimum description length (MDL) principle ! . For statistics beginners, this book is self-contained. The writing style is concise ! . Overall, this is an authoritative source on MDL and a good reference book. Most statisticians would be fortunate to have a copy in their bookshelves." (Thomas C. M. Lee, Journal of the American Statistical Association, Vol. 103 (483), September, 2008) "This book describes the latest developments of the MDL principle. ! The book ! is intended to serve as a readable introduction to the mathematical aspects of the MDL principle when applied to statistical modeling for graduate students in statistics and information sciences. ! Overall, this interesting book will make an important contribution to the field of statistical modeling through the MDL principle." (Prasanna Sahoo, Zentralblatt Math, Vol. 1156, 2009)