Model selection and inference

by Kenneth P. Burnham

We wrote this book to introduce graduate students and research workers in var­ ious scientific disciplines to the use of information-theoretic approaches in the analysis of empirical data. In its fully developed form, the information-theoretic approach allows inference based on more than one model (including estimates of unconditional precision); in its initial form, it is useful in selecting a "best" model and ranking the remaining models. We believe that often the critical issue in data analysis is the selection of a good approximating model that best represents the inference supported by the data (an estimated "best approximating model"). In­ formation theory includes the well-known Kullback-Leibler "distance" between two models (actually, probability distributions), and this represents a fundamental quantity in science. In 1973, Hirotugu Akaike derived an estimator of the (relative) Kullback-Leibler distance based on Fisher's maximized log-likelihood. His mea­ sure, now called Akai