Nothing kills communication like jargon: it signals the tribe you belong to. Jargon makes the distinction between the insiders and the outsiders painfully clear. One particular piece of jargon that has always bothered me is the concept of a “model.” I suppose this has been on my mind recently because I have heard people relay the famous quote from George Box, “All models are wrong, but some are useful.” This is an adage that is hard to escape in Statistics, and like all maxims it becomes trite when overused. I am most annoyed when presenters throw this into their lecture as some legal caveat emptor to mitigate the criticisms of their work….

…But, getting back on topic, what exactly did Box mean by a model? We use this term all the time. Taking a blunt view of Statisticians, all we really do is build models. Of course other scientists also build models, we don’t have a monopoly–yet (insert evil laugh). My definition of a model, albeit inept, is: a description of either an object or a process. Now some descriptions are better than others. A detailed blueprint is a more useful description for building a skyscraper than a poem. This is why mathematical models are so prevalent. They cut directly to a quantitative description without any confusion. Models don’t need to be equations; they can take many different forms, for example a computer program. The important thing is that it is a description.

Joyce’s second blog post discusses two camps of modeling. There are those that want the model to be interpretable and those that do not care about the form of the model but instead only want them to achieve some result, say winning at go or chess. Both are valid descriptions, but they illuminate different aspects of the same object. Neither of them is right and neither of them is wrong. The only flawed assumption is that the only correct description is your own model.

My research deals specifically with what are called surrogate models. These are models that are built and calibrated to produce the same results as another model. Now why would anyone want to do this? It seems meta and academic. Well, you’re not wrong! But there are very good reasons to do this. Simpler models, assuming they have enough fidelity, are easier to analyze and understand without losing relevant information. When thinking about surrogate models I always remember the short story “On Exactitude in Science” by Jorge Luis Borges, which describes an empire whose cartographers were so proficient that their maps were the same size as the empire itself. Every detail of the terrain reproduced exactly. Obviously such a map, although accurate, is rather unwieldy. A cut down version would be sufficient for most practical purposes. The tricky issue is how to perform the trimming.

My surrogate modeling falls into a gray region between the two camps Joyce describes. Often the surrogate model takes the form of some Gaussian Process model that’s inscrutable, and the model being approximated is a computer simulation built up from scientific knowledge. The simulation is understandable but slow, whereas the surrogate is the reverse. The Gaussian Process model is not a better description of the reality that the computer code is stimulating, but it does make certain information available to us that would otherwise be locked away in a computer program running until the end of time. In my case, one model is not enough to describe everything. I believe this plurality is true across Statistics and the other sciences. We must be flexible so we are not dogmatically stuck at the expense of progress.