Mathematical Modelling: Part 2

26 Jun

createModel

Continued on from Mathematical Modelling: Part 1

How do you Model?

Modelling is really  more of art than a science. There is no perfect model. There is no right way to create a model. Anything interesting really depends on having some sort of insight and/or creative thought. But there are ways to guide your thought process.

Whenever I’m trying to create a new model I think:

  • What am I trying to do? Many problem specifications are so vague that you really need to think about what your actual problem is. Before you start doing anything, work out (at least roughly) what you want to be able to do: does it need be able to predict things quickly? Then you want to avoid a problem that takes 3 months to predict tomorrow’s weather.
  • What data do you have? Data could be empirical data or general information like “Weight is relative to height”. Anything that you know straight up to be true (at least in the context of the model)
  • What are the unknowns? I’m including independent variables in here. You might want to model what your wage is in respect to hours worked, make time a independent variable. You might have more than one independent variable.  Besides, chances you have other things you don’t know and need to consult with others to find out. Your model will nearly always have unknowns
  • How can I relate my unknowns and knowns? This is really the essence of modelling, finding some relation between them. What the relationship look like (formula, markov chain, IP….) depends on what you are trying to do (does it it need to be modelled in excel?).
  • What assumptions do I need to make? This comes hand in hand with the previous point. Sure, you try to make do with the information you have, but sometimes you need to make assumptions. Just make sure these assumptions are well justified.

meaningfulResults

So after all of this, hopefully you will have a model. But just because you have a model, doesn’t mean it will be correct. You need to check you model. Questions to ask yourself:

  • Does my model actually model the problem? Cause if it doesn’t, what will it be used for?
  • Does it fit ALL the data I was given? Models are meant to reflect the data, they don’t work if they are not consistent with each other.
  • Did you model all the data? If you left some out, was it for a good reason?
  • Is it written in a usable way? Your model is meant to be used. If people can’t use it, what is the point?
  • Do the predictions make sense? Does it make sense to have a car tire circumference of 1.2km? Nope, if your model says that, you should rethink your model.

Really if any of these are the case, you need to rethink your model.

modelReality

 

Keep in mind there is now right model. There are good models that do what they are meant to and do it well. There are bad models which, well don’t. The only way to get there is to keep on trying.

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