Model Selection and Model Averaging

Model selection throughout the years has remained one of the greatest conundrums in statistical science. In spite of the great advances in modelling from both Bayesian and frequentist perspectives, model selection continues to attract controversies. The most-cited papers in statistics are often related to model comparison methods or consider how to average over different models. This new publication tackles both issues at once in a single volume. Since model selection has a longer history than model averaging, this subject takes a substantially larger part of the book than model averaging, which is covered in only two chapters. After an introduction to the running examples that are used throughout the volume, two separate chapters are dedicated to the two most popular information criteria: Akaike’s and the Bayesian information criterion. Of special interest is Chapter Four, which presents some useful results on the efficiency and consistency of various criteria, including the introduction of some rarely encountered concepts such as the Hannan–Quinn criterion. Model averaging is treated as an extension of model selection, where criteria such as the Akaike or Bayesian information criterion can be used to weight the models under consideration, during sampling. This book is comprehensive in its treatment of the subject and will probably teach something new, even to the most experienced researchers in model selection. In particular, most statisticians will be unfamiliar with the focused information criterion, which is an extension of the idea of ‘focus’ that was introduced by Spiegelhalter et al. (2002), in their seminal paper on the deviance information criterion. The focused information criterion is a fecund new development in the field of model selection, built on the premise that different models may better perform when estimating different types of estimands. The authors have chosen a range of practical examples, which are used throughout the volume, to illustrate the application of the model choice criteria. This will clearly satisfy the practitioners, who require clear illustrations to get started in using these criteria. The more theoretically minded readers, however, will probably need to check some of the original references to deepen their understanding. In particular, the chapter on the Bayesian information criterion would have benefited from a more comprehensive exposition of its links with the Bayes factor, which renders it such a popular criterion in Bayesian circles. Overall, however, the authors have succeeded in bringing together a coherent volume, which gives a state of the art account of the current practice in model selection and comparison, containing a plethora of asymptotic (sometimes new) results, which can be used to compare different model choice criteria. Most importantly, this is the sole volume dedicated to this subject, taking a fully statistical as opposed to an information theoretic approach to the topic of model selection. This book will be attractive to a wide range of graduate students and researchers, users or developers of model choice criteria, of all statistical persuasions.