Model Selection and Model Averaging (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 27)

Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer? Choosing a model is central to all statistical work with data. We have seen rapid advances in model fitting and in the theoretical understanding of model selection, yet this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved with model selection are tackled, with discussions of frequentist and Bayesian methods; model averaging schemes are presented. Real-data examples are complemented by derivations providing deeper insight into the methodology, and instructive exercises build familiarity with the methods. The companion website features Data sets and R code. Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer?" "Choosing a suitable model is central to all statistical work with data. Selecting the variables for use in a regression model is one important example. The past two decades have seen rapid advances both in our ability to fit models and in the theoretical understanding of model selection needed to harness this ability, yet this book is the first to provide a synthesis of research from this active field, and it contains much material previously difficult or impossible to find. In addition, it gives practical advice to the researcher confronted with conflicting results." "Model choice criteria are explained, discussed and compared, including Akaike's information criterion AIC, the Bayesian information criterion BIC and the focused information criterion FIC. Importantly, the uncertainties involved with model selection are addressed, with discussions of frequentist and Bayesian methods. Finally, model averaging schemes, which combine the strengths of several candidate models, are presented."--Jacket

First book to synthesize the research and practice from the active field of model selection.