5.2 The balance between simplicity and accuracy

When choosing between alternative explanations, there is a principle known as Occam’s razor. In very general terms, this principle establishes that given two or more equivalent explanations for the same phenomenon, the simplest is the preferred explanation. A common criterion of simplicity is the number of parameters in a model.

There are many justifications for this heuristic. We are not going to discuss any of them; we are just going to accept them as a reasonable guide.

Another factor that we generally have to take into account when comparing models is their accuracy, that is, how good a model is at fitting the data. According to this criterion, if we have two (or more) models and one of them explains the data better than the other, then that is the preferred model.

Intuitively, it seems that when comparing models, we tend to prefer those that best fit the data and those that are simple. But what should we do if these two principles...