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The abstract concept of "information" can be quantified and this has led to many important advances in the analysis of data in the empirical sciences. This text focuses on a science philosophy based on "multiple working hypotheses" and statistical models to represent them. The fundamental science question relates to the empirical evidence for hypotheses in this set-a formal strength of evidence. Kullback-Leibler information is the information lost when a model is used to approximate full reality. Hirotugu Akaike found a link between K-L information (a cornerstone of information theory) and the maximized log-likelihood (a cornerstone of mathematical statistics). This combination has become the basis for a new paradigm in model based inference. The text advocates formal inference from all the hypotheses/models in the a priori set-multimodel inference.
This compelling approach allows a simple ranking of the science hypothesis and their models. Simple methods are introduced for computing the likelihood of model i, given the data; the probability of model i, given the data; and evidence ratios. These quantities represent a formal strength of evidence and are easy to compute and understand, given the estimated model parameters and associated quantities (e.g., residual sum of squares, maximized log-likelihood, and covariance matrices). Additional forms of multimodel inference include model averaging, unconditional variances, and ways to rank the relative importance of predictor variables.
Introduction--science hypotheses and science philosophy.- Data and models.- Information theory and entropy.- Quantifying the evidence about science hypotheses.- Multimodel inference.- Advanced topics.- Summary.
From the reviews: ".! The writing style is pragmatic and appropriate for someone without advanced statistical training. Readers looking to recommend a book on information-criteria-based modeling to colleagues who are not statisticians, or looking to locate such a book for their libraries are likely to be satisfied with this book. " (Biometrics, December 2008, Brief Reports by the Editor) "This ! book provides an introduction to this approach of evidence-based inference. It is focused on advocating and teaching the approach. It includes some history and philosophy with the methods, and each chapter ends with exercises. ! For those who are already familiar with model-based inference ! it provides a more in-depth account of the information theoretical approach. For those who are new to model-based inference, it provides a good conceptual and technical introduction." (Glenn Suter, Integrated Environmental Assessment and Management, Vol. 5 (2), 2009) "Readership: Researchers and graduate students in ecology and other life sciences. This monograph expounds ideas that the author has developed over many years with Burnham. It is heavily example-based, and aimed at working scientists. Examples are predominately from ecological studies. ! This is an interesting and challenging ! book." (John H. Maindonald, International Statistical Review, Vol. 77 (3), 2009) "!Presents an information-theoretic approach to statistical inference!Well motivated, clearly written, and thought provoking for its targeted readership. !" (The American Statistician, February 2010, Vol. 64, No. 1)