Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach

by Kenneth P. Burnham, David R. Anderson

The second edition of this book is unique in that it focuses on methods for making formal statistical inference from all the models in an a priori set (Multi-Model Inference). A philosophy is presented for model-based data analysis and a general strategy outlined for the analysis of empirical data. The book invites increased attention on a priori science hypotheses and modeling. Kullback-Leibler Information represents a fundamental quantity in science and is Hirotugu Akaike's basis for model selection. The maximized log-likelihood function can be bias-corrected as an estimator of expected, relative Kullback-Leibler information. This leads to Akaike's Information Criterion (AIC) and various extensions. These methods are relatively simple and easy to use in practice, but based on deep statistical theory. The information theoretic approaches provide a unified and rigorous theory, an extension of likelihood theory, an important application of information theory, and are objective and practical to employ across a very wide class of empirical problems. The book presents several new ways to incorporate model selection uncertainty into parameter estimates and estimates of precision. An array of challenging examples is given to illustrate various technical issues. This is an applied book written primarily for biologists and statisticians wanting to make inferences from multiple models and is suitable as a graduate text or as a reference for professional analysts.

Genres: Science, Academic

518 pages, Kindle Edition

First published October 31, 1998

Reviews

[Lucille Nguyen · Rating 5 out of 5]

A classic that brought the information theoretic paradigm to popularity with the English-speaking audience. Somewhat dated, but nonetheless, a statistics text with both practical applications and an eye to the philosophy of inference. A book that is irresistible, irreplaceable, and perhaps the most important book on the subject.

[Usfromdk · Rating 5 out of 5]

Presumably the five star rating is in part due to the amount of work it took to complete the book - in the sense that I probably felt a need to justify having read this book due to the amount of time it took, and if I could convince myself that the book was good this would be an easier thing to do. On the other hand I did make a decision reasonably early on that if I did decide to eventually rate this book, I'd most likely have to give it five stars; the only plausible alternative to giving the book five stars was not rating the book at all - I could never have justified giving this book a low rating even if I'd found myself unable to finish chapter 7, as this would have implied implicitly punishing the authors for basically providing quite exhaustive coverage of the topic(s) at hand.

Some of the content, especially in the later chapters of the book, is quite difficult, especially if you're not willing to spend quite a bit of time on it, but many key ideas are developed and explained in a manner that makes them relatively easy to understand if you have the proper background. A lot of the stuff in this book is stuff it would be easy to argue that people working in the applied sciences ought to know, and it would also not be hard to argue that some of these things (especially the ideas developed in the first few chapters) should likewise be known by non-scientists who would like to hold opinions about science and scientific research.

The book was written some years ago, so some progress has presumably been made in the meantime especially when it comes to concrete applications (due to computing power developments since the book was written - this is probably especially relevant in the context of the application of numerical methods and how to apply the bootstrap) in specific contexts which were not well-explored at the time of the publication of the book. However most of the main points of the book are based on deep theory from information theory and mathematical statistics, so the publication date should not in my mind be considered a strong argument against exploring the ideas presented in this book.

[Peter · Rating 5 out of 5]

Truly inspirational. An incredible text that all researchers working with statistical models should read. One of the later chapters is incredibly technical, but this should not be a deterrent at all. The first half is incredibly useful and clearly illustrates many important points relating information theory and statistics. The introduction of more recent (as of 2002) multi-model inferential methods was incredibly useful. I am surprised by the lack of adoption or understanding of these methods and their nuances in my own field, though that is a completely different story.

If anything, this book has opened my eyes to the rampant misuse of the methods described within: mistakes in model selection and not embracing the uncertainty of the AIC best model. Something that has been known about for two decades!