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This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of 'true' data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression.
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"... this book summarizes his work on a level that requires few mathematical skills ... This treatise comprises a valuable, compact and up-to-date elementary survey of a rapidly growing new field in statistics. Mathematical Reviews, 1992 "The book is a significant contribution to the literature on systems modelling. It represents currently the only comprehensive presentation of the MDL modelling methodology. This is, in my opinion, a powerful methodology, which is likely to play an increasingly important role in the modelling business in the years ahead." Int'l Journal General Systems, 1993
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