Every statistician and data analyst has to make choices. The need arises especially when data have been collected and it is time to think about which model to use to describe and summarise the data. Another choice, often, is whether all measured variables are important enough to be included, for example, to make predictions. Can we make life simpler by only including a few of them, without making the prediction significantly worse?

In this book we present several methods to help make these choices easier. Model selection is a broad area and it reaches far beyond deciding on which variables to include in a regression model.

Two generations ago, setting up and analysing a single model was already hard work, and one rarely went to the trouble of analysing the same data via several alternative models. Thus ‘model selection’ was not much of an issue, apart from perhaps checking the model via goodness-of-fit tests. In the 1970s and later, proper model selection criteria were developed and actively used. With unprecedented versatility and convenience, long lists of candidate models, whether thought through in advance or not, can be fitted to a data set. But this creates problems too. With a multitude of models fitted, it is clear that methods are needed that somehow summarise model fits.