First, apologies for the delay after the overwhelmingly great start and my promises of new posts. I’ve been wanting to write for a week but had other urgent commitments (like teaching) I had to honour first. I hope to post once a week or fortnight, but it will be a bit variable depending on the day job and the interestingness of my activities and thoughts. I do have a lot of ideas lined up – I wouldn’t have started a blog if I didn’t – but at the moment it takes me time to set them down. I expect this to get faster.
Second, thanks for (mostly) sticking to the comments policy and making this a polite, friendly, interesting corner of the web.
Before I begin blogging about models, I ought to talk about what a model is. Aside from the occasional moment of confusion when describing one’s “modelling job” to friends and family, there are several things that might come to mind.
Model is a terribly over-burdened word. It can be an attractive clothes horse, a toy train, something reviewed by Top Gear, or a Platonic ideal. I will talk about three further meanings that relate to the sense of “something used to represent something else”: these are conceptual, statistical, and physical. They are distinct ideas, but in practice they overlap, which can add to the confusion.
A conceptual model is an idea, statement, or analogy that describes or explains something in the real world (or in someone’s imagination). It is ‘abstracted’, simpler than and separated from the thing it describes. In science, before you can do experiments and make predictions you must have an idea, a description, a concept of the thing you are studying. This conceptual model might include, for example, a tentative guess of the way one thing depends on another, which could then be explored with experiments.
A statistical model is a mathematical equation that describes the relationship between two or more things, ‘things’ being more commonly referred to as ‘variables’. A variable is a very broad term for something that varies (ahem), something interesting (or dull) that is studied and predicted by scientists or statisticians*: it could be the number of bees in a garden, the average rainfall in the UK, or the fraction of marine species caught in the North Atlantic that are sharks. A statistical model can often be represented in words as well as equations: for example, ‘inversely proportional’ means that as one variable increases a second variable decreases. The important thing about a statistical model is that it only describes and doesn’t explain.
A physical model is a set of mathematical equations that explains the relationship between two or more variables. It also refers to a computer program that contains these equations, and to help (or increase) the confusion, these computer models are often called simulators. By explain I mean that it is an expression of a theory, a physical law, a chemical reaction, biological process, or cause-and-effect: an expression not only of knowledge but understanding about the way things behave. The understanding might not be perfect – it might be a partial or simplified physical model – but the point is it attempts to describe the mechanisms, the internal cogs and wheels, rather than simply the outward behaviour.
Physical models are the main focus of this blog, but there are many interesting links between the three: physical models often incorporate statistical models to fill in the gaps where our understanding is poor; a statistical model may describe another model (conceptual or physical). There are myriad different types of physical model, and even more uses for them. In the next post, I will talk about a few physical models I use in my research.
A general note about my plans. I think it’s important to first set out some basic terms and concepts, particularly for those that not familiar with modelling, so please be patient if you are an expert. Before long I will also post more technical pieces, which will be labelled as such so as not to scare off non-experts. I’ll also start blogging about the day-to-day, such as interesting conference talks and random (mostly science-related) thoughts, rather than only pre-planned topics.
* The opposite of a variable is…a constant. These can be interesting too.