Defining model performance

OK then, let's ask a question to start talking about performance: when you estimate a model, how do you say if it is a good model? As you have probably already heard, the American statistician George Box used to say:

All models are wrong, but some are useful.

This is, besides a nice quote, also a great truth: there is no perfect model, all models are some kind of an abstraction from reality, like maps are an abstraction from the real Earth. Nevertheless, if those maps are accurate enough, they are invaluable friends in the hands of travelers. This could seem to you nothing more than a suggestive analogy, but it's actually a useful way to intend models since it captures two of their most relevant aspects:

• Models need to have a good level of abstraction from the real phenomenon they are trying to model
• Models have to be accurate enough to be useful

I don't need to say to you that the main topics here are to define what a good level of abstractionis and define what it...