Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach
Springer Science & Business Media, May 28, 2007 - Mathematics - 488 pages
We wrote this book to introduce graduate students and research workers in various scienti?c disciplines to the use of information-theoretic approaches in the analysis of empirical data. These methods allow the data-based selection of a “best” model and a ranking and weighting of the remaining models in a pre-de?ned set. Traditional statistical inference can then be based on this selected best model. However, we now emphasize that information-theoretic approaches allow formal inference to be based on more than one model (m- timodel inference). Such procedures lead to more robust inferences in many cases, and we advocate these approaches throughout the book. The second edition was prepared with three goals in mind. First, we have tried to improve the presentation of the material. Boxes now highlight ess- tial expressions and points. Some reorganization has been done to improve the ?ow of concepts, and a new chapter has been added. Chapters 2 and 4 have been streamlined in view of the detailed theory provided in Chapter 7. S- ond, concepts related to making formal inferences from more than one model (multimodel inference) have been emphasized throughout the book, but p- ticularly in Chapters 4, 5, and 6. Third, new technical material has been added to Chapters 5 and 6. Well over 100 new references to the technical literature are given. These changes result primarily from our experiences while giving several seminars, workshops, and graduate courses on material in the ?rst e- tion.
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A Basis for Model
Basic Use of the InformationTheoretic Approach
Monte Carlo Insights and Extended Examples
Examples and Ideas Illustrated with Linear Regression
Estimation of Density from Line Transect Sampling
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ˆβ ˆθ AIC values AICc approach approximating model assumed Bayesian binomial bootstrap samples candidate models compute concept conditional confidence interval covariance criteria criterion data analysis data dredging data set denoted derived effects evaluation evidence ratio example exponential family fitted model function given global model hence hypothesis testing inference information-theoretic K-L best model K-L distance K-L information likelihood linear model log-likelihood log(g(x matrix methods mixture models model averaging model g model selection uncertainty model set model structure models considered Monte Carlo notation number of parameters overdispersion overfitting parameter estimates parsimonious percentiles prediction predictor variables priori probability distribution QAIC random variable regression relative sample size sampling variance Section selected model selection bias set of candidate set of models simple simulation standard error statistical subset survival probabilities Table theoretical theory trace term true model truth unconditional standard error variation